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%I #4 Mar 30 2012 17:34:55
%S 157,353,8233,23893,26183,30197,63697,118831,131041,150203,152213,
%T 167033,198013,293087,341303,383983,494051,494723,534007,551569,
%U 601949,603541,629203,666697,671287,679417,688907,768203,787207,796867,826039
%N Balanced primes (A090403) of index 4.
%e 353 is a member because 353 = (281 + ...353 + ... + 421)/23
%e = (271 + .. + 353 + ... + 433)/27 = (241 + ... + 353 + ... + 461)/37 = (227 + ... + 353 + ... + 487)/45.
%t f[n_] := Block[{c = 0, k = 1, p = Prime[n], s = Plus @@ Table[ Prime[i], {i, n - 1, n + 1}]}, While[k != n - 1, If[s == (2k + 1)p, c++ ]; k++; s = s + Prime[n - k] + Prime[n + k]]; c]; Prime[ Select[ Range[2, 25797], f[ # ] == 4 &]]
%Y Cf. A096693, A096695, A096705, A096706, A096707, A096709.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jun 28 2004
%E a(17)-a(31) from _Donovan Johnson_, Apr 09 2010
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