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%I #15 Oct 30 2018 10:31:02
%S 31,41,137,277,283,313,353,467,659,937,1201,1291,1409,1427,1543,1567,
%T 1613,1669,1933,2243,2503,2617,2957,3559,3607,3631,4153,4241,5569,
%U 5843,6037,6067
%N Primes p such that p^2 is a sum of 5 successive primes.
%H Zak Seidov, <a href="/A140458/b140458.txt">Table of n, a(n) for n = 1..2000</a>
%e 181+191+193+197+199=31^2, 317+331+337+347+349=41^2, 3733+3739+3761+3767+3769=137^2,...
%t a = {}; For[n = 1, n < 10^4, n++, p1 = Prime[n]; p2 = Prime[n + 1]; p3 = Prime[n + 2]; p4 = Prime[n + 3]; p5 = Prime[n + 4]; p = (p1 + p2 + p3 + p4 + p5)^(1/2); If[PrimeQ[p], AppendTo[a, p]]]; a
%t Sqrt[# ]&/@Select[Total/@Partition[Prime[Range[500000]], 5,1], PrimeQ[ Sqrt[#]]&] (* _Harvey P. Dale_, Nov 12 2011 *)
%t Select[Sqrt[Total/@Partition[Prime[Range[500000]], 5, 1]], PrimeQ] (* _Zak Seidov_, Feb 08 2012 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 26 2008
%E More terms from _Harvey P. Dale_, Nov 12 2011
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