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Smallest prime starting a symmetric n-tuple of consecutive primes of the smallest span (=A266676(n)).
4

%I #35 Jan 25 2025 16:49:42

%S 2,2,3,5,18713,5,12003179,17,1480028129,13,1542186111157,

%T 41280160361347,660287401247633,10421030292115097,3112462738414697093,

%U 996689250471604163,258406392900394343851

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

%C 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).

%C 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.

%C For any n, a(n) <= n or a(n) = A266512(n).

%C a(19) = 9425346484752129657862217. - _Dmitry Petukhov_ and _Anton Nikonov_, Jan 24 2025

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

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

%K nonn,more

%O 1,1

%A _Max Alekseyev_, Jan 01 2016