A055381 - OEIS

%I #31 Jan 13 2024 04:54:03

%S 4,9,12,30,30,165,8021811,1071065190,1613902650,1797595815015,

%T 633925574060895,22930603692243585

%N Smallest composite k such that the n closest primes below and above k are symmetric about k.

%C Center of the smallest 2n-tuple of consecutive odd primes with symmetrical gaps (cf. A055382).

%H Carlos Rivera, <a href="https://www.primepuzzles.net/problems/prob_060.htm">Problem 60. Symmetric primes on each side</a>, The Prime Puzzles & Problems Connection.

%F a(n) = ( A055382(n) + A000040(A000720(A055382(n))+2n) ) / 2 = ( A055382(n) + A151800(...(A151800(A055382(n)))...) ) / 2, where A151800 is iterated 2n times. - _Max Alekseyev_, Jul 23 2015

%F a(n) = (A000040(m) + A000040(m+1))/2, where m = min( {k >= 2 : A359440(k) >= n-1} ). - _Peter Munn_, Jan 09 2023

%e The three primes on each side of 12 (13, 17, 19 and 11, 7, 5) are symmetrical with respect to the gaps, so a(3) = 12.

%t Table[i = n + 2;

%t  While[x =

%t    Differences@

%t     Flatten@{Table[NextPrime[i, k], {k, -n, -1}], i,

%t       Table[NextPrime[i, k], {k, 1, n}]}; x != Reverse[x],

%t i++]; i, {n, 6}] (* _Robert Price_, Oct 12 2019 *)

%Y Cf. A000040, A000720, A001223, A055380, A055382, A151800, A359440.

%K nonn,more,hard

%O 1,1

%A _Jud McCranie_, Jun 23 2000

%E a(10) from _Donovan Johnson_, Mar 09 2008

%E a(11) from _Dmitry Petukhov_, added by _Max Alekseyev_, Aug 08 2014

%E a(12) computed from A055382(12) by _Max Alekseyev_, Jul 23 2015

%E Name clarified by _Peter Munn_, Jan 09 2023