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