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

Author

Max Alekseyev, Dec 30 2015

Keywords

• nonn
• more
• hard

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

• 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.

Crossrefs

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

Formula

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

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