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%I #14 Dec 27 2018 20:06:01
%S 98303927,580868459,784857323,857636141,909894647,951508837,
%T 1367470823,1480028171,1850590099,2106973159,2121382079,2409718043,
%U 2635873907,2704854637,3225527099,3386231579,3823510039,3824915671,3905211517,4123167667,4127991383,4386448117
%N Quadruply balanced primes: primes which are averages of their immediate neighbor primes, their second neighbor primes, their third neighbor primes and their fourth neighbor primes.
%H Donovan Johnson, <a href="/A096710/b096710.txt">Table of n, a(n) for n = 1..1000</a>
%e 98303927 is a member because 98303927 = (98303903 + 98303951)/2 = (98303897 + 98303957)/2 = (98303873 + 98303981)/2 = (98303867 + 98303987)/2.
%t a = {}; Do[p = 2Prime[n]; If[p == Prime[n - 1] + Prime[n + 1], If[ p == Prime[n - 2] + Prime[n + 2], If[p == Prime[n - 3] + Prime[n + 3], If[p == Prime[n - 4] + Prime[n + 4], Print[p/2]; AppendTo[a, p/2]]]]], {n, 6, 117039731}]; a
%t Select[Partition[Prime[Range[207405000]],9,1],(#[[1]]+#[[9]])/2 == (#[[2]]+ #[[8]])/2 == (#[[3]]+#[[7]])/2==(#[[4]]+#[[6]])/2==#[[5]]&][[All,5]] (* _Harvey P. Dale_, Dec 27 2018 *)
%Y Cf. A006562, A051795, A096709, A055380.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jun 28 2004
%E More terms from _Jud McCranie_, Sep 29 2006
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