This is a listing of integer sequences that are esoteric yet interesting, at least to me. It is not at all meant as competition to Sloane's excellent Online Encyclopedia of Integer Sequences. Few of the sequences here are in Sloane's OEIS (or they were not in there at the time they were added here, in most cases) and I don't think they are of general interest. But then again, different people have different ideas of what is esoteric and what is of general interest. Would like to contribute a sequence to this listing? Details on that at the bottom of this page.

Some of the Mathematica commands given below assume that certain functions have been defined,

`Mertens[x_] := Plus @@ MoebiusMu[Range[1, x]]
TriN[x_] := (1/2)(x^2 + x)
SPF[x_] := Take[Flatten[Take[FactorInteger[x]], 1], 1]
BPF[x_] := Take[Take[Flatten[FactorInteger[x]], -2], 1]
DigitalRoot[n_Integer?Positive] := FixedPoint[Plus @@ IntegerDigits[#] &, n]`

as well as the following lists:

`PiDigits50 = RealDigits[N[ Pi, 50]] [[1]]
SGPrimes = Select[Prime[Range[900]], PrimeQ[2# + 1] &]
SafePrimes = Select[Prime[Range[900]], PrimeQ[(# - 1)/2] &]`

If a program has an object called Adddddd (where d are base 10 digits) it refers to a sequence from Sloane's OEIS. Enter (for example) "A012345 = { " then paste the contents of the Sequence: or Signed: field from the appropriate OEIS sequence, making sure to close with " } ".

4001, 4003, 4005, 4007, 4008, 4009, 4011, 4013, 4014, 4016, 4017, 4019, 4020, 4021, 4023, 4024, 4025

Location numbers of my game pieces in the McDonald's Monopoly Best Change Game 2.0. The two more significant digits (40) indicate this is the fourth time McDonald's has had this promotion, while the two less significant digits indicate the position of the piece on the game board (for example, 19 is North Carolina Avenue, 24 is Pennsylvania Railroad).

I have the maximum number of distinct pieces possible to still not win anything. I also had $47 in Best Buy Bucks, but that's money you pay to McDonald's, which McDonald's passes on to Best Buy.

12, 14, 17, 99, 7, 26, 16, 4, 5, 3, 15

Channels on the TV in my hospital room during my convalescence. At first I actually watched something on each of them. Fortunately, I'm well recovered now and the list of TV channels I watch now on my home TV is much shorter: ESPN and PBS.

22, 49, 48, 25, 31, 38, 5, 1, 27, 4, 50, 43, 21, 19, 29, 34, 15, 18, 23, 7, 6, 26, 32, 20, 24, 41, 37, 36, 9, 3, 47, 11, 12, 39, 17, 46, 33, 2, 13, 8, 40, 16, 28, 45, 14, 10, 42, 35, 30, 44

Admission order of the *n*th alphabetical state of the United States.

Alabama is state 1, Alaska is state 2, ... Wyoming is state 50. This sequence is correct for the time period from 1960 to at least 2004.

*World Almanac 2005*

212, 212, 212, 211, 211, 212, 212, 212, 212, 212, 213, 212, 211, 210, 209, 206, 199, 190, 186, 185, 185, 184, 183, 182, 167, 167, 159, 158, 156, 155, 154

Difference between the year a state of the United States had its commemorative statehood quarter and the year it was admitted to the Union.

It is highly unlikely anything will derail the U.S. Mint's schedule. Nevertheless I prefer to stop at the state with the most recent quarter.

10-Year Schedule for Statehood Quarters at the U.S. Mint website.

1, 3, 40, 41, 59, 66, 94, 102, 146, 150, 151, 160, 161, 164, 165, 167, 215, 232, 233, 236, 237, 239, 255, 330, 332, 333, 334, 354, 356, 357, 359, 363, 364, 365, 367, 394, 402, 404, 405, 406, 408, 409, 414, 415, 420, 421, 423, 424, 425, 426, 428, 429, 538, 542, 608, 609, 636, 637, 638, 782, 786, 794, 796, 797, 799, 812, 813, 815, 824, 825, 826, 850, 851, 854, 870, 878, 884, 885, 887, 890, 894, 896, 897, 899, 904, 905, 907, 911, 914, 916, 917, 920, 921

Numbers *n* for which the value of Möbius function and Mertens function are the same. On another page I list the values of Möbius function and Mertens function for the first 2500 integers.

2, 101, 149, 163, 331, 353, 401, 419, 541, 607, 811, 823, 853, 877, 883, 919, 1013, 1279, 1289, 1291, 1297, 1523, 1531, 1543, 1861, 2017, 2099, 2113, 2309, 2689, 3607, 3613, 4603, 4637, 4723, 5107, 5113, 5197, 5261, 5849, 6011, 6067, 6089, 7187, 7853, 7877, 7879, 7901, 7907, 8011, 8017, 9001, 9013, 9203

Prime Mertens function zeroes. This is a subset of Sloane's A028442.

Article in the Wayne State student newspaper on Sloane's OEIS reaching the 100K milestone. »The OEIS works like a search engine. In the search box, one can enter a few terms of the sequence separated by either commas or spaces, for example, Ò5, 7, 11, 23, 47,Ó and it answers with all sequences it finds with those numbers, such as safe primes for the Diffie-Hellman data encryption algorithm in the example above. If a sequence, Ò2, 101, 149, 163,Ó for example, does not match anything in the database, the OEIS gives a link to a form to send the sequence in to Neil Sloane to look at.»

It was here first! Robert Happelberg sent it in to Sloane's OEIS on December 5, 2004, it's Sloane's A100669. Thanks for listing my humble webpage!

3, 41, 59, 66, 102, 151, 165, 167, 233, 239, 255, 354, 357, 359, 367, 402, 406, 409, 421, 426, 429, 609, 638, 782, 786, 797, 826, 854, 885, 887, 890, 894, 897, 907, 911

Numbers *n* for which the value of Möbius function and Mertens function are both -1. Subset of RNTFS00001.

40, 150, 160, 164, 232, 236, 332, 333, 356, 363, 364, 404, 405, 408, 414, 420, 423, 424, 425, 428, 608, 636, 637, 796, 812, 824, 825, 850, 884, 896, 904, 916, 920

Numbers *n* for which the value of Möbius function and Mertens function are both 0. Subset of RNTFS00001.

1, 94, 146, 161, 215, 237, 330, 334, 365, 394, 415, 538, 542, 794, 799, 813, 815, 851, 870, 878, 899, 905, 914, 917, 921

Numbers *n* for which the value of Möbius function and Mertens function are both 1. Subset of RNTFS00001.

1, 5, 3, 25, 2, 16, 142857, 125, 1, 1, 9, 83, 76923, 714285, 6, 625, 588235294117646110, 5, 526315789473684210, 5, 47619, 45

Reciprocal of n multiplied by 10 raised to period length, 1/*n*(10^{p}). Submitted by Anton Mravcek.

This is a problematic sequence. For a while I even thought of describing it as "(10^{p} - 1)/*n* for primes and 10^{p}/*n* for others."

1, 2, 3, 5, 5, 8, 7, 11, 10, 12, 11, 20, 13, 16, 17, 23, 17, 27, 19, 30, 23, 24, 23, 44, 26, 28, 31, 40, 29, 50, 31, 47, 35, 36, 37, 67, 37, 40, 41, 66, 41, 66, 43, 60, 57, 48, 47, 92, 50, 63

Sum of divisors of *n* minus cototient of *n*.

5, 11, 19, 29, 41, 5, 71, 89, 109, 131, 5, 181, 11, 239, 271, 5, 11, 379, 419, 461, 5, 19, 599, 11, 701, 5, 811, 11, 929, 991, 5, 19, 29, 1259, 11, 5, 1481, 1559, 11, 1721, 5, 31, 1979, 2069, 2161, 5, 2351, 31, 2549

Smallest prime factor of *n*^{2} + (*n* - 1). First *n* is *n* = 2. This sequence is almost the same as smallest prime factor of *n*^{2} - (*n* + 1) Terms of this sequence that match Sloane's A028387 and are prime are listed in Sloane's A002327.

7, 13, 3, 31, 43, 3, 73, 7, 3, 7, 157, 3, 211, 241, 3, 307, 7, 3, 421, 463, 3, 7, 601, 3, 19, 757, 3, 13, 7, 3, 7, 1123, 3, 13, 31, 3, 1483, 7, 3, 1723, 13, 3, 7, 19, 3, 37, 13, 3, 2551

Smallest prime factor of *n*^{2} + (n + 1). First *n* is *n* = 2. This sequence is almost the same as smallest prime factor of *n*^{2} - (n - 1) Terms of this sequence that match Sloane's A002061, the central polygonal numbers, are prime and are listed in Sloane's A002383.

11, 3, 31, 41, 3, 61, 71, 3, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 13, 23, 3, 43, 53, 3, 73, 83, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5

Smallest prime factor of reversal of digits of *n*. First *n* is *n* = 11. Reversal of digits of *n* is listed in Sloane's A004086.

2, 3, 5, 7, 20, 21, 38, 39, 56, 57, 74, 75, 92, 93, 95, 110, 111, 128, 129, 133, 146, 147, 164, 165, 182, 183, 185, 200, 201, 218, 219, 236, 237, 254, 255, 259, 272, 273, 275, 290, 291, 308, 309, 326, 327, 344, 345, 362, 363, 365, 380, 381, 398, 399, 416, 417, 434, 435, 452, 453, 455, 470, 471, 488, 489, 506, 507, 511, 524, 525, 542, 543, 545, 560, 561, 578, 579, 596, 597, 614, 615, 632, 633, 635, 637, 650, 651, 668, 669, 686, 687, 704, 705, 722, 723, 725, 740, 741, 758, 759, 763, 776, 777, 794, 795, 812, 813, 815, 830, 831, 848, 849, 866, 867, 884, 885, 889, 902, 903, 905, 920, 921, 938, 939, 956, 957, 974, 975, 992, 993, 995

Numbers *m* such that digital root of *m* matches smallest prime factor of *m*.

Alonso Delarte noticed that if you isolate the even numbers in this sequence, all terms are 18 apart. Looking at just the odd numbers this way, 18 shows up a lot, but not exclusively.

2, 3, 5, 7, 12, 48, 50, 70, 128, 192, 196, 320, 448, 500, 700, 768

Numbers *n* such that digital root of n matches largest prime factor of *n*.

23, 47, 59, 83, 167, 839, 2099, 5879, 6719

Safe primes that are also highly cototient numbers.

2, 23, 83, 89, 113, 419, 509, 659, 1049, 1889, 3359, 4409

Sophie Germain primes that are also highly cototient numbers.

2, 3, 5, 3, 13, 5, 7, 73, 5, 241, 433, 13, 577, 7, 1153, 11, 43, 29, 7, 8641, 41, 11, 7, 30241, 17, 61, 47, 31, 13, 11, 103681, 73, 161281, 13, 7, 241921, 19, 41, 293, 11

Smallest prime factor of the *n*th highly totient number plus 1.

Flatten[SPF[A097942 + 1]]

2, 3, 5, 15, 13, 35, 65, 73, 185, 241, 433, 527

Smallest totient answer for the *n*th highly totient number.

When a highly totient number is followed by that prime, that prime will obviously be the smallest totient answer for that particular highly totient number.

4, 8, 8, 158, 788, 788, 210998, 5316098, 34415168, 703693778

Smallest composite number such that the next *n* - 1 integers have the property that the list of smallest prime factors not in common with a smaller number of the set is the set of the first *n* prime numbers.

A simpler description for this sequence would be nice. If the description sounds confusing (and I bet it does), the chart below might help clarify the concept.

Integer | Factorization | Smallest unique prime factor |
---|---|---|

210998 | 2 × 105499 | 2 |

210999 | 3 × 61 × 1153 | 3 |

211000 | 2^{3} × 5^{3} × 211 | 5 |

211001 | 7 × 43 × 701 | 7 |

211002 | 2 × 3 × 11 × 23 × 139 | 11 |

211003 | 13 × 16231 | 13 |

211004 | 2^{2} × 17 × 29 × 107 | 17 |

4, 9, 10, 161, 792, 793, 211004, 5316105, 34415176, 703693787

Smallest composite number such that the previous *n* - 1 integers have the property that the list of smallest prime factors not in common with a smaller number of the set is the set of the first *n* prime numbers.

3, 7, 13, 19, 31, 37, 67, 109, 127, 139, 157, 181, 199, 211, 307, 337, 379, 409, 487, 499

Chen primes not of the form 3*n* - 1 (that is, not Eisenstein primes without imaginary parts).

3, 6, 30, 585, 870

Value of *n*th Markov triple, with the Markov triples sorted in order by largest integer included.

2, 5, 7, 13, 19, 31, 61, 181, 199

"So not Stern primes," for lack of a better name. Primes *q* such that *q* - 2*n*^{2} is prime for every 2*n*^{2} < *q*.

Laurent Hodges, *A lesser-known Goldbach conjecture*.

5993, 6797, 59117, 59117, 87677, 148397

The largest odd number that can be represented as the sum of a prime and twice a square in no more than *n* - 1 ways. First *n* is 1.

This sequence comes from Hodges's conjecture that for every
number *n* > 1 there are only a finite number of odd integers that cannot be represented as the sum of a prime and twice a square in at least *n* ways. Hodges expects any further terms of this sequence to be congruent to 2 mod 3.

Laurent Hodges, *A lesser-known Goldbach conjecture*.

3, 3, 13, 19, 55, 61, 139, 139, 181, 181, 391, 439, 559, 619, 619, 829, 859, 1069

The smallest odd number that can be represented as the sum of a prime and twice a square in at least *n* ways.

Hodges expects any further terms of this sequence to be congruent to 1 mod 3 (as are all known terms except the 3s at the beginning).

Laurent Hodges, *A lesser-known Goldbach conjecture*.

3, 139, 181, 619, 2 341, 3 331, 4 189, 4 801, 5 911, 6 319, 8 251, 9 751, 11311

The smallest odd number that can be represented as the sum of a prime and twice a square in at least ways *n* for more than one value of *n*.

Laurent Hodges, *A lesser-known Goldbach conjecture*.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Sylvester-type sequence starting with 0. Submitted by Anton Mravcek.

Thanks to Alonso Delarte for this program.

Numerically, for *n* = 0 forward, this sequence is the same as Sloane's A057427. This sequence is undefined for negative *n*, while A057427(n) = -1 for all negative *n*.

For more sequences of this sort, see Sylvester-type sequences.

Even though for most practical purposes you only need π to 10 or so decimal places (heck, I've even done some "good enough" estimates with π as exactly 3), professional and amateur mathematicians alike study π to hundreds or thousands, sometimes millions, of decimal places. Will all this help you design a better tire or bake a better cake? Probably not. So for this reason, I consider integer sequences based on the decimal digits of π to be esoteric.

For our purposes here, we will consider the integer part of π, 3, to belong to the sequence of decimal digits of π (as listed in Sloane's A000796) unless otherwise noted. We will consider that initial 3 to be at position 0, unless otherwise noted.

3, 31, 653, 4159, 14159

First substring of *n* digits of π that spells a prime number. For example, for *n* = 3, the first substring of 3 digits, 314, is clearly not prime. Neither is 141, 415, and so on until we get to 653.

For more sequences of this sort, see Digits of π.

1, 2, 4, 8, G, W, 1S, 3K, 74, E8, SG, 1KW, 35S, 6BK, CN4, PA8, 1EKG, 2T4W, 5M9S, B8JK, MH34, 18Y68, 2HWCG, 4ZSOW, 9ZLDS, JZ6RK, 12YDJ4, 27WR28, 4FTI4G, 8VN08W, HRA0HS, ZIK0ZK, 1Z141Z4, 3Y238Y8, 7W4G7WG, FS8WFSW, VKHSVLS, 1R4ZLR7K, 3I9Z7IF4, 70JYF0U8, E13WU1OG

Powers of 2 written in base 36. Submitted by Numerao.

ア, イ, エ, ク, タ, ミ, アチ, イメ, オナ, コユ, ナリ, ヨヒ, アロキ, ウムセ, キテフ, セレケ, ヘマツ, アシソ, アシソラ, イネマノ, オイタウ, コエミカ, トケチシ, ロツメネ, アムリニア, ウトヒウイ, カヤクヤオ

Powers of 2 written in base 47. Submitted by Alonso Delarte.

Since the characters 0 - 9 and A - Z are not enough for base 47, Japanese katakana are co-opted for this purpose. A is 1, I is 2, U is 3, E is 4 and O is 5. Then KA is 6, KI is 7, KU is 8, KE is 9 and KO is 10. Syllable groups with line changes are ignored for this purpose. So then we use SA for 11, TA for 16, NA for 21, HA for 26, MA for 31, RA for 36, YA for 41, YU for 42, YO for 43, WA for 44, WO for 45 and N for 46. Alonso Delarte suggested using a kanji for 0, but I prefer to keep it simple and use 0 here. As a digit it does not occur here like it does in base 10 and how it certainly does in base 2, but then again, I'm taking Alonso's word that this sequence is correct.

1, 2, 6, 16, 35, 66, 112, 176, 261, 370, 506, 672, 871, 1106, 1380, 1696, 2057, 2466, 2926, 3440, 4011, 4642, 5336, 6096, 6925, 7826, 8802, 9856, 10991, 12210

The *n*^{th} *n*-gonal number. First *n* is *n* = 1.

This one is already in Sloane's OEIS, it's A060354.

Of course 1- and 2-gonal numbers don't have much of a basis in geometric reality, but they are included here for the sake of completeness.

0, 0, 3, 12, 30, 60, 105, 168, 252, 360, 495

The *n*^{th} n-gonal number minus *n*.

After executing the command to calculate the *n*^{th} *n*-gonal number (see NNGON00001), execute this command:

1, 48, 142, 283, 471, 706, 988, 1317, 1693, 2116, 2586, 3103, 3667, 4278, 4936, 5641, 6393, 7192, 8038, 8931, 9871, 10858, 11892, 12973, 14101, 15276, 16498, 17767, 19083, 20446, 21856, 23313, 24817, 26368, 27966, 29611, 31303, 33042, 34828, 36661, 38541, 40468, 42442, 44463, 46531, 48646, 50808, 53017, 55273, 57576

Centered 47-gonal numbers.

1, 48, 186, 460, 915, 1596, 2548, 3816, 5445, 7480, 9966, 12948, 16471, 20580, 25320, 30736, 36873, 43776, 51490, 60060, 69531, 79948, 91356, 103800, 117325, 131976, 147798, 164836, 183135, 202740, 223696, 246048, 269841, 295120, 321930, 350316, 380323, 411996, 445380, 480520, 517461, 556248, 596926, 639540, 684135, 730756, 779448, 830256, 883225, 938400

Pyramidal 47-gonal numbers.

After executing the command to calculate regular 47-gonal numbers (see RPOLY00047), execute this command:

1, 47, 138, 274, 455, 681, 952, 1268, 1629, 2035, 2486, 2982, 3523, 4109, 4740, 5416, 6137, 6903, 7714, 8570, 9471, 10417, 11408, 12444, 13525, 14651, 15822, 17038, 18299, 19605, 20956, 22352, 23793, 25279, 26810, 28386, 30007, 31673, 33384, 35140, 36941, 38787, 40678, 42614, 44595, 46621, 48692, 50808, 52969, 55175

Regular 47-gonal numbers.

Alonso Delarte points out that this sequence was on OEIS predating this listing. It's Sloane's A095311, added by Gary Adamson on June 2, 2004. The sequence is even discussed in an old book from the 1960s!

1, 1730, 5188, 10375, 17291, 25936, 36310, 48413, 62245, 77806, 95096, 114115, 134863, 157340, 181546, 207481, 235145, 264538, 295660, 328511, 363091, 399400, 437438, 477205, 518701, 561926, 606880, 653563, 701975, 752116, 803986, 857585, 912913, 969970, 1028756, 1089271, 1151515, 1215488, 1281190, 1348621, 1417781, 1488670, 1561288, 1635635, 1711711, 1789516, 1869050, 1950313, 2033305, 2118026

Centered 1729-gonal numbers. Submitted by Anton Mravcek.

1, 1729, 5184, 10366, 17275, 25911, 36274, 48364, 62181, 77725, 94996, 113994, 134719, 157171, 181350, 207256, 234889, 264249, 295336, 328150, 362691, 398959, 436954, 476676, 518125, 561301, 606204, 652834, 701191, 751275, 803086, 856624, 911889, 968881, 1027600, 1088046, 1150219, 1214119, 1279746, 1347100, 1416181, 1486989, 1559524, 1633786, 1709775, 1787491, 1866934, 1948104, 2031001, 2115625

1729-gonal numbers.

1, 69106, 207316, 414631, 691051, 1036576, 1451206, 1934941, 2487781, 3109726, 3800776, 4560931, 5390191, 6288556, 7256026, 8292601, 9398281, 10573066, 11816956, 13129951, 14512051, 15963256, 17483566, 19072981, 20731501, 22459126, 24255856, 26121691, 28056631, 30060676, 32133826, 34276081, 36487441, 38767906, 41117476, 43536151, 46023931, 48580816, 51206806, 53901901, 56666101, 59499406, 62401816, 65373331, 68413951, 71523676, 74702506, 77950441, 81267481, 84653626

Centered 69105-gonal numbers.

1, 69105, 207312, 414622, 691035, 1036551, 1451170, 1934892, 2487717, 3109645, 3800676, 4560810, 5390047, 6288387, 7255830, 8292376, 9398025, 10572777, 11816632, 13129590, 14511651, 15962815, 17483082, 19072452, 20730925, 22458501, 24255180, 26120962, 28055847, 30059835, 32132926, 34275120, 36486417, 38766817, 41116320, 43534926, 46022635, 48579447, 51205362, 53900380, 56664501, 59497725, 62400052, 65371482, 68412015, 71521651, 74700390, 77948232, 81265177, 84651225

Regular 69105-gonal numbers.

These sequences are of course infinite, but for my convenience, I only plan to go up to about 1000 in each chain, and up to the self number closest to 200.

The initial terms of the following sequences correspond to the self numbers (Sloane's A003052).

1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, 77, 91, 101, 103, 107, 115, 122, 127, 137, 148, 161, 169, 185, 199, 218, 229, 242, 250, 257, 271, 281, 292, 305, 313, 320, 325, 335, 346, 359, 376, 392, 406, 416, 427, 440, 448, 464, 478, 497, 517, 530, 538, 554, 568, 587, 607, 620, 628, 644, 658, 677, 697, 719, 736, 752, 766, 785, 805, 818, 835, 851, 865, 884, 904, 917, 934, 950, 964, 983, 1003

Chain of digit addition generators with initial term 1. After initial term, each term is equal to the previous term plus the sum of its digits.

Thanks to Alonso Delarte for this program. He writes that this program can easily be modified for any other digit addition generator chain, and in fact, I have used it for each of the following chains.

This sequence is Sloane's A004207.

For more sequences of this sort, see Digit Addition Generator Chains.

These are sequences of fractions split into numerators and denominators, in much the same way as is done in the OEIS. I usually use an arbitrary cut-off of 50.

1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 1, 2, 15, 16, 17, 18, 1, 20, 3, 22, 23, 24, 25, 2, 27, 4, 29, 30, 31, 32, 33, 34, 5, 36, 37, 2, 3, 40, 41, 6, 43, 44, 45, 46, 47, 48, 7, 50

Numerators of *n*/1729.

1729, 1729, 1729, 1729, 1729, 1729, 247, 1729, 1729, 1729, 1729, 1729, 133, 247, 1729, 1729, 1729, 1729, 91, 1729, 247, 1729, 1729, 1729, 1729, 133, 1729, 247, 1729, 1729, 1729, 1729, 1729, 1729, 247, 1729, 1729, 91, 133, 1729, 1729, 247, 1729, 1729, 1729, 1729, 1729, 1729, 247, 1729

Denominators of *n*/1729.

MCDXLIV, MCDXLVI, MCDLXIV, MCDLXVI, MDCXLIV, MDCXLVI, MDCLXIV, MDCLXVI

(1444, 1446, 1464, 1466, 1644, 1646, 1664, 1666)

Numbers that in Roman numerals use every numeral exactly once and in a valid way. Submitted by Robert Happelberg.

Numbers like 1364 are not in this sequence. We could certainly try to parse a combination like CMDXLIV (1364), but this is a combination that would have never arisen in the ancient Roman times. (Some other invalid combinations, however, do yield numbers that are in this sequence, e.g., CMXDILV, which can be parsed as 1444).

0, 6, 8, 9, 69, 88, 96, 609, 689, 808, 906, 986, 6009, 6889, 8008, 8698, 8888, 8968, 9006, 9886

Numbers that are strobogrammatic in base 10 written in ASCII using a Base 14 font such as Times New Roman or Courier New.

This is a subset of Sloane's A000787 which is plainly called "strobogrammatic numbers" but would be more properly called "strobogrammatic numbers written in a font where the digits 1, 6, 8 and 9 are strobogrammatic."

60, 68, 80, 86, 89, 90, 98, 600, 606, 608, 660, 666, 668, 669, 680, 686, 688, 690, 696, 698, 699, 800, 806, 809, 860, 866, 868, 869, 890, 896, 898, 900, 908, 909, 960, 966, 968, 969, 980, 988, 990, 996, 998, 999

Numbers that are quasi-strobogrammatic (read like a different number upside down, but still a valid one in the representational scheme) in base 10 written in ASCII using a Base 14 font such as Times New Roman or Courier New.

The only practical use for this sequence, as far as I can tell, is in contexts where a number might need to read upside down, such as on lottery balls and aircraft carriers. In such cases, it becomes necessary to draw a line under the number, or if possible, to write out the number in words as well as numerals to avoid any confusion.

136, 138, 146, 148, 156, 158, 163, 164, 165, 167, 169, 176, 178, 183, 184, 185, 186, 187, 189, 196, 198, 236

Numbers whose digits have all possible different heights when written in a font like Georgia.

0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101, 102, 110, 111, 112, 120, 121, 122, 200, 201, 202, 210, 211, 212, 220, 221, 222

Numbers that are the same height as a lowercase x when written in a font like Georgia.

Interestingly, this sequence is in Sloane's OEIS, A007089, but arising out of a different problem of numerical representation.

3, 4, 5, 7, 9, 33, 34, 35, 37, 39, 43, 44, 45, 47, 49, 53, 54, 55, 57, 59, 73, 74, 75, 77, 79, 93, 94, 95, 97, 99

Numbers that are the same height as a lowercase x when written in a font like Georgia.

6, 8, 66, 68, 86, 88, 666, 668, 686, 688, 866, 868, 886, 888

Numbers that are the same height as a capital letter when written in a font like Georgia.

200, 202, 204, 205, 206, 208, 320, 322, 324, 325, 326, 328, 510, 512, 514, 515, 516, 518, 620, 622, 624, 625, 626, 628, 840, 842, 844, 845, 846, 848, 890, 892, 894, 895, 896, 898

Unprimeable numbers in base 10, composite numbers that can't be turned prime by changing just one digit.

If changing two digits is allowed, then all of these are primeable. All the odd numbers in this sequence, at least in the range I've examined, end in 5. At this point I can't answer the question: is there an odd unprimeable number ending in 1, 3, 7 or 9?

226, 234, 241, 249, 250, 258, 269, 277, 278, 281, 287, 293, 295, 298, 299, 304, 305, 306, 316, 324, 326, 329, 331, 332, 334, 338, 339, 346, 348, 349, 356, 361, 363, 368, 378, 380, 386, 387, 388, 389, 391, 393, 394, 395, 396, 397, 398

Numbers with question marks (???) in What's Special About This Number? as of September 21, 2004. Submitted by Robert Happelberg.

134, 136, 138, 139, 141, 143, 146, 148, 149, 152, 154, 156, 158, 159, 161, 162, 164, 165, 166, 168, 171, 172, 173, 174

Integers without articles in Wikipedia's List of numbers as of December 13, 2004.

Of course this sequence is infinite. The English Wikipedia will probably eventually have articles on every integer between -1 and +1024. Only very few integers beyond that range will get their own articles.

1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2

Term a(1) in Sloane's Online Encyclopedia of Integer Sequences sequence A*n*.

Although this sequence is finite, it is still (being at least 100000 terms) too long to list here. I looked at the first twenty sequences. A(1) of A000004, A000014 are both zeroes, while A(1) of A000020 is 2. This sequence is now itself in the OEIS, A100544.

1, 2, 3, 5, 6, 8, 10, 14, 16, 19, 26, 27, 36, 37

Sequences in Sloane's Online Encyclopedia of Integer Sequences in which the A number is a member of the sequence (leading zeroes ignored).

For example, Sloane's A002808 lists composite numbers. We can be sure 2808 is a composite number, even though it's not displayed in the sequence field. (Though of course it makes it easier for me if the number is small enough, or has an index small enough, to be listed in the sequence field).

I don't know how to compute A000019, the number of primitive groups of degree *n*, but I followed the link entitled "The first 1000 terms," and sure enough, 19 occurs a couple of times after the last number listed in the sequence field.

This one was in the OEIS long before it was here. It's A053873.

4, 7, 9, 11, 12, 13, 15, 17?, 18, 20, 21, 22, 23, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43

Sequences in Sloane's Online Encyclopedia of Integer Sequences in which the A number is not a member of the sequence (leading zeroes ignored).

This one was in the OEIS long before it was here. It's A053169.

For example, Sloane's A000040 lists the prime numbers, but 40 is itself not a prime number.

4, 7, 12, 35, 56, 66, 82, 118, 132, 141, 143, 144, 145, 152, 156, 252, ..., 290, ..., 384, ..., 567, ..., 578, 580, 581, 582, 583, 584, ..., 1014, 1015, ..., 1106, 1107, ..., 2808, ..., 8586, 8588, 8590, 8591, 8592, 8594, 8596, 8597, 8598, 8600, 8602, ..., 18252, ..., 97785, ..., 100766, 100767, ..., 105416

Sequences in Sloane's Online Encyclopedia of Integer Sequences that are primefree.

Ten different people wrote me to point out that I had mistakenly included 566 in the list. Numerao's e-mail had the earliest timestamp, so he gets the credit for the correction. Thanks for pointing out my mistake. I have now corrected it.

Alonso Delarte, relayed a question as to whether or not terms beyond the "clipping" range count, to which I reply, yes, they do. Thus, if Paul Hoffman's inverted version of the Wilf primefree sequence was in the OEIS, its A number would not be a member of this sequence. That even though there would only be room to display about the first half dozen terms or so, which are large composite numbers. (Eric W. Weisstein, of Mathworld, had long ago noticed that the 138th term of that sequence is a prime).

At about the same time I received the fifth e-mail with the correction, this sequence was added to the OEIS as A111157. There, only the terms up to 252 are listed, as ellipses are not allowed in the OEIS (I too hesitated to use them, but I can afford to be informal). If you have the time and the inclination to eliminate any of these ellipses, feel free to e-mail me (but if you eliminate the first ellipse, contact the OEIS first).

In case you're wondering, 111157 is now a term of A053169.

For a professional mathematician, the term "primefree" refers specifically to a Fibonacci-like sequence that does not contain primes, such as Wilf's *a*_{1} = 20615674205555510, *a*_{2} = 3794765361567513, *a*_{n} = *a*_{n - 1} + *a*_{n - 2}. I use the term for any sequence that does not contain primes, even if the lack of primes is a trivial consequence of the definition of the sequence (for example, the sequence of multiples of 4, A008586).

For the sake of this sequence, I regard 1 as not a prime number.

16, 6, 9, 9, 9, 12, 10, 12, 7, 10, 21, 14, 19, 19, 24, 12, 12, 8, 12, 15

Homeruns batted by National League homerun leader in the year 1900 + n.

13, 16, 13, 10, 8, 12, 8, 7, 9, 10, 9, 10, 13, 9, 7, 12, 9, 11, 29, 54

Homeruns batted by American League homerun leader in the year 1900 + n.

1985, 1955, 1985, 2015, 1985, 1955, 1885, 1985

The years Marty McFly travels through in the *Back To The Future* trilogy.

1969, 1972, 1984, 1996

Years travelled to by a Federation starship which correspond to the present year when the *Star Trek* episode aired or the movie premiered.

I'm not entirely sure this sequence is correct, so I'm hoping a *Star Trek* fan will write in and set the record straight.

If you would like to add a sequence to this listing, you can e-mail me at primefan@yahoo.com. If the sequence appears to be of limited practical value and I find it interesting, I will add it. But if on the other hand, it appears to be of high practical value, I will recommend to you that you submit it to Sloane's OEIS.