A051070 -id:A051070 - cp's OEIS frontend

A031214 Initial term of sequence An.

0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 2, 8, 14, 4, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 4, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1

Offset: 1

Jeff Burch

This ignores the offset and gives the first term of the actual entry.
Since the sequences in the OEIS occasionally change their initial terms (for editorial reasons), this is an especially ill-defined sequence! - N. J. A. Sloane, Jan 01 2005
Sequences like this are deprecated. - Joerg Arndt, Apr 16 2020

			A000001 begins 0,1,1,1,2,1,2,1,5,2,... so a(1) = 0 = a(31214).

PrimeFan, Esoteric Integer Sequences
PrimeFan, Esoteric Integer Sequences [Cached copy]
N. J. A. Sloane, Online Encyclopedia of Integer Sequences
Index entries for sequences whose definition involves A_n (or An).

Cf. A039928, A051070, A091967, A107357, A102288; also A000001, A000002, A000003, A000004, A000005, etc.

Data updated by Sean A. Irvine, Apr 16 2020

A107357 a(n) = 1 + A_n(n), or a(n) = -1 if sequence A_n is not defined up to index n.

Original entry on oeis.org

2, 3, 2, 1, 3, 4, 1, 8, 9, 5, 64, 2, 317, 79, 17, 2049, 7653, 26628, 9, 24001, 232920, 1145407, 3498690007594650042369, 2058538, 59, 27, 28, 60, 9272781, 4, 69273669, 4870848, 2387010102192469724605148123694256129, 2, 2, -52, 44, 1, -4695, 174, 44584, 111111111111111111111111111111111111111112, 30402458, 668803782, 1134903171, 382443020333

Offset: 1

N. J. A. Sloane, May 25 2005

sign

What is a(107357)?

See A051070, A091967, A102288 for more about this type of sequence.

N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 21.
Index entries for sequences whose definition involves A_n (or An).

a(n) = A051070(n) + 1 (except when A_n has fewer than n terms). See also A091967 and A102288 (the same but ignoring the offset).

Definition revised by N. J. A. Sloane, Nov 27 2016
Definition rephrased by M. F. Hasler, Jan 20 2017
Corrected a(36) and a(42), extended to a(46) by M. F. Hasler, Jan 21 2017

A091967 a(n) is the n-th term of sequence A_n, ignoring the offset, or -1 if A_n has fewer than n terms.

Original entry on oeis.org

0, 2, 1, 0, 2, 3, 0, 6, 6, 4, 44, 1, 180, 42, 16, 1096, 7652, 13781, 8, 24000, 119779, 458561, 152116956851941670912, 1054535, -53, 26, 27, 59, 4806078, 2, 35792568, 3010349, 2387010102192469724605148123694256128, 2, 0, -53, 43, 0, -4097, 173, 37338, 111111111111111111111111111111111111111111, 30402457, 413927966

Offset: 1

Proposed by several people, including Jeff Burch and Michael Joseph Halm

sign

This version ignores the offset of A_n and just counts from the beginning of the terms shown in the OEIS entry.
Thus a(8) = 6 because A_8 begins 1,1,2,2,3,4,5,6,... [even though A_8(8) is really 7].
The value a(n) = -1 could arise in two different ways, but it will be easy to decide which. - N. J. A. Sloane, Nov 27 2016
From M. F. Hasler, Sep 22 2013: (Start)
The value of a(91967) can be chosen at will.
Note that this sequence may change if the initial terms in A_n are altered, which does happen from time to time, usually because of the addition of an initial term.
After a(47), currently unknown, the sequence continues with a(48) = A48(47) = 1497207322929, a(49) = A49(48) = unknown, a(50) = A50(49) = unknown, a(51) = A51(50) = 1125899906842625, a(52)=97, a(53) = -1 (since A000053 has only 29 terms). (End)
a(58) = A000058(57) = 138752...985443 (29334988649136302 digits) is too large to include in the b-file. - Pontus von Brömssen, May 21 2022

			a(1) = 0 since A000001 has offset 0, and begins with A000001(0) = 0.
a(26) = 26 because the 26th term of A000026 = 26.

Pontus von Brömssen, Table of n, a(n) for n = 1..57 (terms n = 1..46 from M. F. Hasler)
OEIS, List of finite sequences, sorted by A-number.
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
Index entries for sequences whose definition involves A_n (or An).

See A051070, A107357, A102288 for other versions.

Cf. A000001, A000002, A000003, A000004, A000005, A000006, A000007, A000008, A000009, A000010, A000011, A000012, A000013, A000014, A000015, etc.

Corrected and extended by Jud McCranie; further extended by N. J. A. Sloane and E. M. Rains, Dec 08 1998
Corrected and extended by N. J. A. Sloane, May 25 2005
a(26), a(36) and a(42) corrected by M. F. Hasler, Jan 30 2009
a(43) and a(44) added by Daniel Sterman, Nov 27 2016
a(1) corrected by N. J. A. Sloane, Nov 27 2016 at the suggestion of Daniel Sterman
Definition and comments changed by N. J. A. Sloane, Nov 27 2016

A102288 a(n) = 1 + (the n-th term in sequence A_n, ignoring the offset), or a(n) = -1 if A_n has fewer than n terms.

Original entry on oeis.org

1, 3, 2, 1, 3, 4, 1, 7, 7, 5, 45, 2, 181, 43, 17, 1097, 7653, 13782, 9, 24001, 119780, 458562, 152116956851941670913, 1054536, -52, 27, 28, 60, 4806079, 3, 35792569, 3010350, 2387010102192469724605148123694256129, 3, 1, -52, 44, 1, -4096, 174, 37339, 111111111111111111111111111111111111111112, 30402458, 413927967

Offset: 1

Alexandre Wajnberg, Feb 19 2005

sign

a(n) = A091967(n) + 1, except when A_n has fewer than n terms, in which case a(n) = -1. Of course this means that a value a(n) = -1 could arise in two different ways, but it will be easy to decide which. - N. J. A. Sloane, Nov 27 2016
What is a(102288)?!
See A091967 and A051070 for much more about this type of sequence. See A107357 for the variant which respects the offset of A_n (and therefore isn't affected when a sequence is completed by missing initial values).
The definition of this sequence is used in the traditional 'diagonal' proof that there are uncountably many integer sequences. - Simon Nickerson (simonn(AT)maths.bham.ac.uk), Jun 28 2005
The term a(102288) has no possible value according to the present definition, so the definition of this term should be changed, including the possibility that the sequence is defined to be finite, with fewer than 102288 terms. (In that case, the (former, impossible) definition which would say that a(102288) = -1 because A102288 has fewer than 102288 terms, does not apply.) - The term a(47) is currently unknown, since A000047 is known only up to n = 35. - M. F. Hasler, Jan 20 2017
I disagree with the previous comment! I prefer the present, deliberately paradoxical, definition. - N. J. A. Sloane, Jan 20 2017

			a(53) = -1 since A000053 has only 29 terms.

M. F. Hasler, Table of n, a(n) for n = 1..46
Index entries for sequences whose definition involves A_n (or An).

a(n) = A091967(n) + 1. See also A051070, A107357 (the same but respecting the offset).

Corrected and extended by N. J. A. Sloane, May 25 2005
Offset corrected by M. F. Hasler, Sep 22 2013
Corrected and extended by Daniel Sterman, Nov 27 2016
Definition revised by N. J. A. Sloane, Nov 27 2016
a(1) fixed by Daniel Sterman, Nov 28 2016
a(26) corrected by M. F. Hasler, Jan 20 2017

A031135 Incorrect version of A091967.

Original entry on oeis.org

1, 2, 1, 0, 2, 3, 0, 6, 8, 4, 63, 1, 316, 42, 16, 2048, 7652, 13781, 8, 24000, 11977, 458561, 152116956851941670912, 1054535, 53, 26, 27, 59, 4806078, 3, 35792568, 3010349, 2387010102192469724605148123694256128, 2, 0, 53, 43, 0

Offset: 1

dead

Probably because of changes in the offsets of certain sequences, this is now incorrect. See A051070, A091967, A107357, A102288 for better versions.

A358291 a(n) = smallest k not already in the sequence such that OEIS entry Ak contains n.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 9, 15, 10, 11, 13, 19, 17, 18, 14, 26, 16, 21, 20, 27, 22, 25, 37, 28, 56, 62, 47, 36, 48, 32, 29, 40, 61, 51, 44, 69, 24, 59, 113, 46, 33, 52, 41, 57, 73, 70, 68, 55, 80, 134, 53, 115, 93, 49, 50, 45, 78, 98, 66, 54, 31, 43, 64, 83, 79, 94, 84

Offset: 0

N. J. A. Sloane, Nov 30 2022

			A000001 contains 0, so a(0) = 1.
A000002 contains 1, so a(1) = 2.
k = 10 is the smallest k not yet in the sequence such that Ak = A000010 contains 8, so a(8) = 10.

Index entries for sequences whose definition involves A_n (or An).

Cf. A051070, A053169, A053873.

More terms from Hugo Pfoertner, Dec 01 2022

cp's OEIS Frontend

A031214 Initial term of sequence An.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A107357 a(n) = 1 + A_n(n), or a(n) = -1 if sequence A_n is not defined up to index n.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A091967 a(n) is the n-th term of sequence A_n, ignoring the offset, or -1 if A_n has fewer than n terms.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A102288 a(n) = 1 + (the n-th term in sequence A_n, ignoring the offset), or a(n) = -1 if A_n has fewer than n terms.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A031135 Incorrect version of A091967.

Views

Author

Keywords

Comments

A358291 a(n) = smallest k not already in the sequence such that OEIS entry Ak contains n.

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions