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.

Showing 1-3 of 3 results.

A266583 Smallest prime starting a symmetric n-tuple of consecutive primes of the smallest span (=A266676(n)).

Original entry on oeis.org

2, 2, 3, 5, 18713, 5, 12003179, 17, 1480028129, 13, 1542186111157, 41280160361347, 660287401247633, 10421030292115097, 3112462738414697093, 996689250471604163, 258406392900394343851, 824871967574850703732309, 9425346484752129657862217, 824871967574850703732303
Offset: 1

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Author

Max Alekseyev, Jan 01 2016

Keywords

Comments

An n-tuple (p(1),...,p(n)) is symmetric if p(k)+p(n+1-k) is the same for all k=1,2,...,n (cf. A175309).
In contrast to A266512, n-tuples here may be singular and give the complete set of residues modulo some prime. For example, for n=3 we have the symmetric 3-tuple: (3,5,7) = (3,3+2,3+4), but there are no other symmetric 3-tuples of the form (p,p+2,p+4), since one of its elements would be divisible by 3.
For any n, a(n) <= n or a(n) = A266512(n).

Links

Crossrefs

Cf. A055380, A065688, A175309, A266511, A266512, A261324.

Formula

a(n) = A000040(A266585(n)).

Extensions

a(18)-a(20) added by Dmitry Petukhov, Feb 15 2025

A266676 Smallest span (difference between the start and end) of a symmetric n-tuple of consecutive primes.

Original entry on oeis.org

0, 1, 4, 8, 36, 14, 60, 26, 84, 34, 132, 46, 168, 56, 180, 74, 240, 82
Offset: 1

Views

Author

Max Alekseyev, Jan 02 2016

Keywords

Comments

An n-tuple (p(1),...,p(n)) is symmetric if p(k)+p(n+1-k) is the same for all k=1,2,...,n (cf. A175309).
In contrast to A266511, n-tuples here may be singular and give the complete set of residues modulo some prime. For example, for n=3 we have the symmetric 3-tuple: (3,5,7) = (3,3+2,3+4) of span a(3)=4, but there are no other symmetric 3-tuples of the form (p,p+2,p+4), since one of its elements would be divisible by 3.
a(n) <= A266511(n).

Crossrefs

The smallest starting primes and their indices of the corresponding tuples are given in A266583 and A266585.
Cf. A055380, A065688, A175309, A266511, A266512, A261324.

A266584 Smallest m such that prime(m) starts a (nonsingular) symmetric n-tuplet of consecutive primes of the smallest span (=A266511(n)).

Original entry on oeis.org

1, 2, 15, 3, 2136, 4, 788244, 7, 73780392, 6, 57067140928, 1361665032086, 19953429852608, 290660101635794, 74896929428416952, 24660071077535201, 5620182896687887031
Offset: 1

Views

Author

Max Alekseyev, Jan 01 2016

Keywords

Comments

See A266583 for further comments and the relation to A266585.
A000040(a(n)+n-1) - A000040(a(n)) = A266511(n).

Crossrefs

Cf. A055380, A065688, A175309, A266511, A266512, A261323, A261324, A266583, A266585.

Formula

a(n) = A000720(A266512(n)).

Extensions

More terms from Max Alekseyev, Jul 24 2019
Showing 1-3 of 3 results.

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