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

%I A055380 #71 Mar 25 2025 10:12:01
%S A055380 5,18731,683783,98303927,60335249959,1169769749219,3945769040699039,
%T A055380 159067808851610657,6919940122097246597
%N A055380 Central prime p in the smallest (2n+1)-tuple of consecutive primes that are symmetric with respect to p.
%C A055380 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.
%C A055380 a(9) <= 6919940122097246597. The solution was found by the BOINC project "SPT test project". - _Natalia Makarova_, Nov 25 2023
%C A055380 a(n) is the smallest number m such that A346399(m) = 2n + 1. - _Ya-Ping Lu_, May 12 2024
%H A055380 Stop@home, <a href="http://stop.inferia.ru/">BOINC project</a> to search all up to 2^64. [Dead link]
%H A055380 Symmetric Prime Tuples, <a href="https://boinc.termit.me/adsl/">SPT test project</a>.
%F A055380 a(n) = A151800^(n)(A175309(2n)), i.e., A151800 applied n times on A175309(2n). - _Max Alekseyev_, Jul 26 2014
%e A055380 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.
%e A055380 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).
%t A055380 Table[i = n + 2;
%t A055380  While[x = Differences[Table[Prime[k + i], {k, -n, n}]];
%t A055380 x != Reverse[x], i++]; Prime[i], {n, 3}] (* _Robert Price_, Oct 12 2019 *)
%Y A055380 Cf. A001223, A055381, A055382, A006562, A051795, A081415, A096710, A346399.
%K A055380 more,nonn
%O A055380 1,1
%A A055380 _Jud McCranie_, Jun 23 2000
%E A055380 a(6) from _Donovan Johnson_, Mar 09 2008
%E A055380 Definition corrected by _Max Alekseyev_, Jul 29 2014
%E A055380 a(7) from _Dmitry Petukhov_, added by _Max Alekseyev_, Nov 03 2014
%E A055380 a(8) from SPT project, added by _Dmitry Petukhov_, Apr 06 2017
%E A055380 a(9) from SPT project, added by _Dmitry Petukhov_, Mar 25 2025