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A051795 Doubly balanced primes: primes which are averages of both their immediate and their second neighbors.

%I A051795 #38 Jun 22 2024 18:15:51
%S A051795 18731,25621,28069,30059,31051,44741,76913,97441,103669,106681,118831,
%T A051795 128449,135089,182549,202999,240491,245771,249199,267569,295387,
%U A051795 347329,372751,381401,435751,451337,455419,471521,478099,498301,516877,526441,575231,577873
%N A051795 Doubly balanced primes: primes which are averages of both their immediate and their second neighbors.
%C A051795 Could also be called overbalanced or [3,5]-balanced primes: balanced primes which are equally average of 3,5 consecutive prime neighbors as follows: a(n)=[q+a(n)+r]/3=[p+q+a(n)+r+s]/5 See 3-balanced=A006562;[3,5,7]-balanced=A081415. - _Labos Elemer_, Apr 02 2003
%C A051795 Numbers m such that A346399(m) is odd and >= 5. - _Ya-Ping Lu_, May 11 2024
%H A051795 Jud McCranie and Sebastian Petzelberger, <a href="/A051795/b051795.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Jud McCranie)
%e A051795 25621 belongs to the sequence because 25621 = (25609 + 25633)/2 = (25603 + 25609 + 25633 + 25639)/4.
%t A051795 Transpose[Select[Partition[Prime[Range[50000]],5,1],(#[[1]]+#[[5]])/2 == (#[[2]]+#[[4]])/2 == #[[3]]&]][[3]] (* _Harvey P. Dale_, Sep 13 2013 *)
%o A051795 (Python)
%o A051795 from sympy import nextprime; p, q, r, s, t = 2, 3, 5, 7, 11
%o A051795 while t < 580000:
%o A051795     if p + t == q + s == 2*r: print(r, end = ', ')
%o A051795     p, q, r, s, t = q, r, s, t, nextprime(t) # _Ya-Ping Lu_, May 11 2024
%Y A051795 Cf. A006562, A081415, A096710, A055380, A346399.
%K A051795 easy,nonn
%O A051795 1,1
%A A051795 _Harvey P. Dale_, Dec 10 1999