cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A072887 The s-inners or non-s-aints, numbers generated like the Aronson series from the letters, specifically the s, in a generating sentence, "S ain't the second, third, fourth, fifth . . . letter of this sentence.".

Original entry on oeis.org

1, 9, 31, 36, 98, 107, 156, 164, 210, 221, 266, 312, 358, 365, 407, 417, 461, 468, 510, 520, 548, 556, 564, 566, 571, 577, 587, 598, 608, 613, 618, 623, 630, 641, 651, 661, 671, 673, 680, 686, 698, 711, 723, 730, 735, 742, 749, 762, 792, 800, 846, 857, 905
Offset: 1

Views

Author

Michael Joseph Halm, Jul 29 2002

Keywords

Comments

The discovery of the s-inners was inspired by the mention of the Aronson series in Douglas R. Hofstadter's Metamathematical Themas.

Examples

			a(1)= 1 because the first letter in the generating sentence that is s is the first one, a.

Links

Crossrefs

Cf. A005224.
Complement of A072886.

Formula

In blocks of 10 letters: saintthese condthirdf ourthfifth sixthseven theighthte nthelevent htwelfthth irteenthfo urteenthfi fteenthsix teenthseve nteentheig hteenthnin ...

Extensions

a(15) onward corrected by Sean A. Irvine, Nov 02 2024

A080519 Positions of the letter t in the French phrase enumerating these positions, "T est la première, quatrième, dix-huitième, trentième, trente-cinquième,... lettre dans cette phrase...".

Original entry on oeis.org

1, 4, 18, 30, 35, 39, 44, 48, 59, 63, 79, 84, 96, 101, 113, 129, 131, 146, 162, 169, 173, 182, 189, 201, 203, 213, 214, 226, 231, 243, 244, 248, 251, 261, 268, 280, 287, 300, 307, 320, 327, 329, 341, 345, 352, 364, 368, 375, 391, 393, 407, 408, 424, 425
Offset: 1

Views

Author

N. J. A. Sloane, Mar 21 2003

Keywords

Comments

The phrase ends "... où les espaces, les virgules et les traits d'union ne comptent pas." This means that spaces, commas and hyphens are not counted.
French version of A005224.

Examples

			"T est la première, quatrième, dix-huitième, trentième, ... lettre de cette phrase..." has a 't' in 1st, 4th, 18th, 30th, ... position.
But the dots represent an infinite list of words: In contrast to the versions starting with another letter (except for 'e', 'i' and 'm' which share this property), the phrase cannot be finite, because each term adds at least 2 't's on the average. This will remain true even after reaching "mille" (thousand), "un million", "un milliard", ... because these t-less words occur almost always accompanied by coefficients between 1 and 1000.

Links

Crossrefs

Cf. Aronson's sequence A005224, A080517-A080520.

Programs

  • PARI
    {c=0; apply(x -> x>"@" & c++ & x=="t" & print1(c","), Vec("t est la premiere, quatrieme, dix-huitieme, trentieme, trente-cinquieme, trente-neuvieme, quarante-quatrieme, quarante-huitieme, cinquante-neuvieme, soixante-troisieme, soixante-dix-neuvieme, quatre-vingt-quatrieme, quatre-vingt-seizieme, cent et unieme, cent treizieme, cent vingt-neuvieme cent trente et unieme, cent quarante-sixieme, cent soixante-deuxieme, cent soixante-neuvieme, cent soixante-treizieme, cent quatre-vingt-deuxieme, cent quatre-vingt-neuvieme, deux cent et unieme, deux cent troisieme, deux cent treizieme,..."));}  \\ M. F. Hasler, Sep 30 2011

A091387 Aronson's mod 13 sequence: "T is the first, fourth, eleventh, third, ... letter in this sentence, not counting spaces or commas and all mod 13".

Original entry on oeis.org

1, 4, 11, 3, 11, 0, 11, 4, 12, 5, 7, 12, 4, 11, 0, 5, 11, 6, 12, 4, 12, 4, 6, 11, 4, 6, 11, 4, 9, 4, 10, 2, 10, 3, 8, 1, 3, 6, 1, 4, 6, 2, 8, 9, 4, 10, 2, 7, 6, 11, 4, 6, 9, 9, 1, 9, 2, 7, 12, 4, 10, 1, 1, 3, 8, 1, 3, 6, 12, 4, 5, 1, 7, 8, 3, 5, 10, 3, 8, 1, 7, 0, 2, 10, 12, 2, 4, 0, 6, 12, 5, 0, 3, 5
Offset: 0

Views

Author

Sam Alexander, Jan 05 2004

Keywords

Comments

Infinite? Periodic? It seems the answers are "Yes and No" because many numbers (such as "tenth") have multiple T's and moreover, in many of these, the T's are spread such that at least one of them will be != 2 mod 13 (2 is important because "second" is the only T-less word)

References

  • A. J. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.

Links

Crossrefs

Cf. A005224, A091388, A091389, A091390, A091391.

A091388 Aronson's mod 14 sequence: "T is the first, fourth, eleventh, third,... letter in this sentence, not counting spaces and commas and all mod 14".

Original entry on oeis.org

1, 4, 11, 3, 11, 0, 11, 4, 12, 5, 7, 12, 4, 11, 0, 5, 11, 6, 12, 4, 12, 4, 6, 11, 4, 6, 11, 4, 9, 4, 10, 2, 10, 3, 8, 1, 3, 6, 1, 4, 6, 2, 8, 9, 4, 10, 2, 7, 6, 11, 4, 6, 9, 9, 1, 9, 2, 7, 12, 4, 10, 1, 1, 3, 8, 1, 3, 6, 12, 4, 5, 1, 7, 8, 3, 5, 10, 3, 8, 1, 7, 0, 2, 10, 12, 2, 4, 0, 6, 12, 5, 0, 3, 5
Offset: 0

Views

Author

Sam Alexander, Jan 05 2004

Keywords

Comments

Infinite? Periodic? It seems the answers are "Yes and No" because many numbers (such as "tenth") have multiple T's and moreover, in many of these, the T's are spread such that at least one of them will be != 2 mod 14 (2 is important because "second" is the only T-less word)
Is this the same as A091387? - R. J. Mathar, Aug 27 2025

References

  • A. J. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.

Links

Crossrefs

Cf. A005224, A091387, A091389, A091390, A091391.

A091389 Aronson's mod 15 sequence: "T is the first, fourth, eleventh, first, ... letter in this sentence, not counting spaces and commas and all mod 15".

Original entry on oeis.org

1, 4, 11, 1, 9, 0, 4, 10, 1, 3, 6, 12, 13, 6, 8, 13, 0, 4, 8, 13, 4, 6, 10, 14, 5, 11, 2, 4, 8, 12, 3, 8, 10, 13, 4, 8, 13, 6, 3, 9, 11, 1, 3, 12, 14, 2, 4, 8, 12, 3, 9, 11, 0, 4, 9, 11, 4, 12, 3, 4, 9, 14, 5, 9, 6, 12, 14, 4, 6, 14, 7, 13, 4, 9, 2, 8, 10, 0, 2, 11, 1, 7, 11, 1, 6, 11, 13, 3, 9, 13
Offset: 0

Views

Author

Sam Alexander, Jan 05 2004

Keywords

Comments

Infinite? Periodic? It seems the answers are "Yes and No" because many numbers (such as "tenth") have multiple T's and moreover, in many of these, the T's are spread such that at least one of them will be != 2 mod 15 (2 is important because "second" is the only T-less word)

References

  • A. J. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.

Links

Crossrefs

Cf. A005224, A091387, A091388, A091390, A091391.

A091390 Aronson's mod 16 sequence: "T is the first, fourth, eleventh, zeroth, ... letter in this sentence, not counting spaces or commas and all mod 16".

Original entry on oeis.org

1, 4, 11, 0, 8, 14, 4, 10, 14, 4, 6, 9, 15, 3, 9, 14, 3, 8, 12, 14, 6, 12, 0, 2, 11, 13, 2, 8, 12, 1, 3, 8, 14, 12, 14, 2, 6, 2, 4, 9, 15, 0, 9, 15, 3, 5, 10, 0, 4, 15, 11, 0, 5, 9, 15, 4, 9, 13, 15, 7, 9, 12, 2, 8, 13, 1, 9, 15, 4, 9, 14, 2, 8, 13, 15, 3, 7, 12, 0, 7, 12, 14, 3, 15, 1, 5, 9, 15, 3
Offset: 0

Views

Author

Sam Alexander, Jan 05 2004

Keywords

Comments

Infinite? Periodic? It seems the answers are "Yes and No" because many numbers (such as "tenth") have multiple T's and moreover, in many of these, the T's are spread such that at least one of them will be != 2 mod 16 (2 is important because "second" is the only T-less word)

References

  • A. J. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.

Links

Crossrefs

Cf. A005224, A091387, A091388, A091389, A091391.

A091391 Aronson's mod 17 sequence: "T is the first, fourth, eleventh, sixteenth, seventh, ... letter in this sentence, not counting spaces and commas and all mod 17".

Original entry on oeis.org

1, 4, 11, 16, 7, 12, 16, 6, 8, 13, 1, 5, 10, 16, 1, 5, 9, 15, 2, 4, 7, 12, 16, 5, 9, 14, 2, 6, 1, 8, 10, 15, 3, 7, 12, 0, 6, 10, 4, 10, 15, 0, 3, 8, 12, 14, 7, 9, 14, 3, 8, 10, 13, 2, 4, 7, 12, 16, 5, 7, 16, 1, 6, 12, 16, 6, 11, 0, 4, 6, 15, 0, 3, 5, 9, 13, 8, 15, 0, 5, 10, 14, 2, 9, 14, 1, 7, 11
Offset: 0

Views

Author

Sam Alexander, Jan 05 2004

Keywords

Comments

Infinite? Periodic? It seems the answers are "Yes and No" because many numbers (such as "tenth") have multiple T's and moreover, in many of these, the T's are spread such that at least one of them will be != 2 mod 17 (2 is important because "second" is the only T-less word)

References

  • A. J. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.

Links

Crossrefs

Cf. A005224, A091387, A091388, A091389, A091390.

A096828 Numbers that must appear in any variation of A097390.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25
Offset: 1

Views

Author

Matthew Vandermast, Aug 13 2004

Keywords

Comments

These are also the numbers that must appear an infinite number of times in any A097390-like sequence (in English). For the numbers that can possibly appear infinitely often in such a sequence, see A096829.
Also, numbers that appear in A097395.

Examples

			The number 1, not listed here, also appears in A097390, since the sentence on which A097390 is based ("This sentence contains the twentieth, eighth, ninth ... letters of the English alphabet, in order.") includes the word "contains," which includes "a," the first letter of the English alphabet. But this need not have been the case. Had the sentence begun: "This sentence is composed of ...", for example, 1 would not have been a member of the resulting sequence.

Crossrefs

Cf. A005224, A097389, A097390, A096829, A097395.

A096829 Numbers that can appear an infinite number of times in a variation of A097390.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 12, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25
Offset: 1

Views

Author

Matthew Vandermast, Aug 13 2004

Keywords

Examples

			The number 12 appears infinitely often in any sequence based on a variation of the A097390 sentence ("This sentence contains the twentieth, eighth, ninth ... letters of the English alphabet, in order") that contains a "k" or "l" in the prologue (e.g. "This sentence, amazingly, contains the twentieth, eighth, ninth ..."). Otherwise, it does not appear at all. The other members of the sequence must appear infinitely often in any sequence based on any English variation of A097390 that generates an infinite string of ordinal number-words (cf. A096828).

Crossrefs

Cf. A005224, A097389, A097390, A096828, A097395.

A097389 Numbers that appear in A097390.

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 8, 9, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25
Offset: 1

Views

Author

Matthew Vandermast, Aug 13 2004

Keywords

Comments

All numbers listed appear an infinite number of times except 1, which appears once.

Crossrefs

Cf. A005224, A096828, A097390, A096829, A097395.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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