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

4, 9, 12, 30, 30, 165, 8021811, 1071065190, 1613902650, 1797595815015, 633925574060895, 22930603692243585, 5179852391836339140, 9648166508472058455

Offset: 1

Author

Jud McCranie, Jun 23 2000

Keywords

• nonn
• more
• hard

Comments

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

Examples

			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.
		

Links

• Carlos Rivera, Problem 60. Symmetric primes on each side, The Prime Puzzles & Problems Connection.

Crossrefs

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

Programs

Mathematica

Table[i = n + 2;
 While[x =
   Differences@
    Flatten@{Table[NextPrime[i, k], {k, -n, -1}], i,
      Table[NextPrime[i, k], {k, 1, n}]}; x != Reverse[x],
i++]; i, {n, 6}] (* Robert Price, Oct 12 2019 *)

Formula

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

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

Extensions

a(10) from Donovan Johnson, Mar 09 2008

a(11) from Dmitry Petukhov, added by Max Alekseyev, Aug 08 2014

a(12) computed from A055382(12) by Max Alekseyev, Jul 23 2015

Name clarified by Peter Munn, Jan 09 2023

a(13)-a(14) computed from A055382 by Dmitry Petukhov, Mar 25 2025