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

1,1

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

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

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.

Formula

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

Crossrefs

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

Sequence in context: A080669 A099205 A051005 * A002163 A093422 A297890

Adjacent sequences: A266580 A266581 A266582 * A266584 A266585 A266586

Keyword

nonn,more,changed

Author

Max Alekseyev, Jan 01 2016

Extensions

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

Status

approved