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

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

Offset: 1

Author

Max Alekseyev, Jan 01 2016

Keywords

• nonn
• more

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

• 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 forum.

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