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

1,1

Comments

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

Links

Table of n, a(n) for n=1..20.

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.

Formula

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

Crossrefs

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

Sequence in context: A191996 A171079 A097929 * A041501 A163488 A215536

Adjacent sequences: A266509 A266510 A266511 * A266513 A266514 A266515

Keyword

nonn,more,hard,changed

Author

Max Alekseyev, Dec 30 2015

Extensions

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

Status

approved