cp's OEIS Frontend

A055381 Smallest composite k such that the n closest primes below and above k are symmetric about k.

%I A055381 #39 Mar 26 2025 17:22:14
%S A055381 4,9,12,30,30,165,8021811,1071065190,1613902650,1797595815015,
%T A055381 633925574060895,22930603692243585,5179852391836339140,
%U A055381 9648166508472058455
%N A055381 Smallest composite k such that the n closest primes below and above k are symmetric about k.
%C A055381 Center of the smallest 2n-tuple of consecutive odd primes with symmetrical gaps (cf. A055382).
%H A055381 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 A055381 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 A055381 a(n) = (A000040(m) + A000040(m+1))/2, where m = min( {k >= 2 : A359440(k) >= n-1} ). - _Peter Munn_, Jan 09 2023
%e A055381 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 A055381 Table[i = n + 2;
%t A055381  While[x =
%t A055381    Differences@
%t A055381     Flatten@{Table[NextPrime[i, k], {k, -n, -1}], i,
%t A055381       Table[NextPrime[i, k], {k, 1, n}]}; x != Reverse[x],
%t A055381 i++]; i, {n, 6}] (* _Robert Price_, Oct 12 2019 *)
%Y A055381 Cf. A000040, A000720, A001223, A055380, A055382, A151800, A359440.
%K A055381 nonn,more,hard
%O A055381 1,1
%A A055381 _Jud McCranie_, Jun 23 2000
%E A055381 a(10) from _Donovan Johnson_, Mar 09 2008
%E A055381 a(11) from _Dmitry Petukhov_, added by _Max Alekseyev_, Aug 08 2014
%E A055381 a(12) computed from A055382(12) by _Max Alekseyev_, Jul 23 2015
%E A055381 Name clarified by _Peter Munn_, Jan 09 2023
%E A055381 a(13)-a(14) computed from A055382 by _Dmitry Petukhov_, Mar 25 2025