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

Offset

1,1

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

Links

Table of n, a(n) for n=1..8.

Stop@home, BOINC project to search all up to 2^64. [Dead link]

Symmetric Prime Tuples, SPT test project.

Formula

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

Example

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).

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 *)

Crossrefs

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

Sequence in context: A263684 A358810 A191940 * A201002 A246870 A193366

Adjacent sequences: A055377 A055378 A055379 * A055381 A055382 A055383

Keyword

more,nonn

Author

Jud McCranie, Jun 23 2000

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

Status

approved