A055380 Central prime p in the smallest (2n+1)-tuple of consecutive primes that are symmetric with respect to p.

5, 18731, 683783, 98303927, 60335249959, 1169769749219, 3945769040699039, 159067808851610657, 6919940122097246597

Offset: 1

Author

Jud McCranie, Jun 23 2000

Keywords

• more
• nonn

Comments

Least n-tuply balanced primes: primes which are averages of both their immediate neighbors, their second neighbors, their third neighbors, ... and their n-th neighbors.

a(9) <= 6919940122097246597. The solution was found by the BOINC project "SPT test project". - Natalia Makarova, Nov 25 2023

a(n) is the smallest number m such that A346399(m) = 2n + 1. - Ya-Ping Lu, May 12 2024

Examples

			In 5-tuple of consecutive primes (18713, 18719, 18731, 18743, 18749), the primes are symmetric w.r.t. its central prime 18731, since 18713+18749 = 18719+18743 = 2*18731, and this is the smallest such 5-tuple. Hence, a(2)=18731.
Alternatively, the symmetry can be seen from the differences between consecutive primes. For (18713, 18719, 18731, 18743, 18749), the differences are (6,12,12,6).
		

Links

• Stop@home, BOINC project to search all up to 2^64. [Dead link]
• Symmetric Prime Tuples, SPT test project.

Crossrefs

Cf. A001223, A055381, A055382, A006562, A051795, A081415, A096710, A346399.

Programs

Mathematica

Table[i = n + 2;
 While[x = Differences[Table[Prime[k + i], {k, -n, n}]];
x != Reverse[x], i++]; Prime[i], {n, 3}] (* Robert Price, Oct 12 2019 *)

Formula

a(n) = A151800^(n)(A175309(2n)), i.e., A151800 applied n times on A175309(2n). - Max Alekseyev, Jul 26 2014

Extensions

a(6) from Donovan Johnson, Mar 09 2008

Definition corrected by Max Alekseyev, Jul 29 2014

a(7) from Dmitry Petukhov, added by Max Alekseyev, Nov 03 2014

a(8) from SPT project, added by Dmitry Petukhov, Apr 06 2017

a(9) from SPT project, added by Dmitry Petukhov, Mar 25 2025