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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..12.

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

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A283105 A179808 A083351 * A287498 A359301 A174911

Adjacent sequences: A055378 A055379 A055380 * A055382 A055383 A055384

Keyword

nonn,more,hard

Author

Jud McCranie, Jun 23 2000

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

Status

approved