A102288 -id:A102288 - 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

A051070 a(n) is the n-th term in sequence A_n, respecting the offset, or a(n) = -1 if A_n has fewer than n terms.

Original entry on oeis.org

1, 2, 1, 0, 2, 3, 0, 7, 8, 4, 63, 1, 316, 78, 16, 2048, 7652, 26627, 8, 24000, 232919, 1145406, 3498690007594650042368, 2058537, 58, 26, 27, 59, 9272780, 3, 69273668, 4870847, 2387010102192469724605148123694256128, 1, 1, -53, 43, 0, -4696, 173, 44583, 111111111111111111111111111111111111111111, 30402457, 668803781, 1134903170, 382443020332

Offset: 1

Robert G. Wilson v, Aug 23 2000

a(58) = A000058(58) = 192523...920807 (58669977298272603 digits) is too large to include in the b-file. - Pontus von Brömssen, May 19 2022
Comment from N. J. A. Sloane, Dec 26 2022 (Start)
Note that a(n) = -1 can arise in two ways: either A_n has fewer than n terms, or A_n has at least n terms, but its n-th term is -1.
Here is a summary of the terms with n <= 80.
a(n) = -1 occurs just twice, for n = 53 and 54, in both cases because the relevant New York subway lines do not have enough stops.
a(1) though a(65) are known, although a(58) = = 192523...920807 has 58669977298272603 digits.
a(66) is the first unknown value.
Also unknown for n <= 80 are a(67), a(72), a(74), a(75), a(76), and a(77) (counts of numbers <= 2^n represented by various quadratic forms; some of these do not even have b-files), and a(80), which like a(66) is a graph-theory question. (End)

			a(19) = 8 because A000019(19) = 8.
a(20) = 24000 because A000020(20) = 24000.

Seth A. Troisi, Table of n, a(n) for n = 1..57 (terms 1..48 from Pontus von Brömssen).
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
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).

See A091967, A107357, A102288 for other versions. See also A031214, A031135.

Cf. A000019, A000020, A000058.

for m from 1 do
  url:= sprintf("https://oeis.org/A%06d/b%06d.txt",m,m);
  S:= URL:-Get(url);
  L:= StringTools[Split](S,"\n");
  for t in L do
    g:= sscanf(t, "%d %d");
    if nops(g) = 2 and g[1] = m then
      a[m]:= g[2];
      break
    fi;
  od;
  if not assigned(a[m]) then break fi;
od:
seq(a[i],i=1..m-1); # Robert Israel, May 31 2015

Rechecked and 4 more terms added by N. J. A. Sloane, May 25 2005
a(36) and a(42) corrected and a(43) to a(46) added by Robert Israel, May 31 2015
Definition revised by N. J. A. Sloane, Nov 27 2016

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

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.

cp's OEIS Frontend

A031214 Initial term of sequence An.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A051070 a(n) is the n-th term in sequence A_n, respecting the offset, or a(n) = -1 if A_n has fewer than n terms.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

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

A031135 Incorrect version of A091967.

Views

Author

Keywords

Comments