A266584 -id:A266584 - cp's OEIS frontend

A266512 Smallest prime starting a (nonsingular) symmetric n-tuplet of the shortest span (=A266511(n)).

2, 3, 47, 5, 18713, 7, 12003179, 17, 1480028129, 13, 1542186111157, 41280160361347, 660287401247633, 10421030292115097, 3112462738414697093, 996689250471604163, 258406392900394343851, 824871967574850703732309, 9425346484752129657862217, 824871967574850703732303

Offset: 1

Max Alekseyev, Dec 30 2015

A similar sequence that allows singular symmetric n-tuples is given in A266583.
a(1)-a(10) from Natalia Makarova
a(11)-a(14), a(16) from Dmitry Petukhov
a(15), a(17) from Jaroslaw Wroblewski

N. Makarova and Carlos Rivera, Problem 62. Symmetric k-tuples of consecutive primes, The Prime Puzzles & Problems Connection.
Natalia Makarova and Vladimir Chirkov, Theoretical patterns with a minimal diameter for a(2) - a(50)
Dmitry Petukhov, Anton Nikonov and Ruslan Vikulov, found a(19) and proof of that is smallest (in Russian), posts in Symmetric tuples of consecutive primes on dxdy blog.

Cf. A055380, A065688, A175309, A266511, A266583, A266584.

a(n) = A000040(A266584(n)).

a(18) from Jaroslaw Wroblewski
a(20) from Natalia Makarova and Jaroslaw Wroblewski
a(19) from Dmitry Petukhov, Anton Nikonov and Ruslan Vikulov, Jan 24 2025

A266585 Smallest m such that prime(m) starts a symmetric n-tuple of consecutive primes of the smallest span (=A266676(n)).

Original entry on oeis.org

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

Offset: 1

Max Alekseyev, Jan 01 2016

See A266583 for further comments and the relation to A266584.

A000040(a(n)+n-1) - A000040(a(n)) = A266676(n).

Cf. A055380, A065688, A175309, A266511, A266512, A261323, A261324, A266583, A266584.

a(n) = A000720(A266583(n)).

More terms from Max Alekseyev, Jul 24 2019

cp's OEIS Frontend

A266512 Smallest prime starting a (nonsingular) symmetric n-tuplet of the shortest span (=A266511(n)).

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