A140458 Primes p such that p^2 is a sum of 5 successive primes.

31, 41, 137, 277, 283, 313, 353, 467, 659, 937, 1201, 1291, 1409, 1427, 1543, 1567, 1613, 1669, 1933, 2243, 2503, 2617, 2957, 3559, 3607, 3631, 4153, 4241, 5569, 5843, 6037, 6067

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..2000

Example

181+191+193+197+199=31^2, 317+331+337+347+349=41^2, 3733+3739+3761+3767+3769=137^2,...

Mathematica

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
Sqrt[# ]&/@Select[Total/@Partition[Prime[Range[500000]], 5, 1], PrimeQ[ Sqrt[#]]&] (* Harvey P. Dale, Nov 12 2011 *)
Select[Sqrt[Total/@Partition[Prime[Range[500000]], 5, 1]], PrimeQ] (* Zak Seidov, Feb 08 2012 *)

Crossrefs

Sequence in context: A040987 A040180 A158754 * A364149 A101520 A225862

Adjacent sequences: A140455 A140456 A140457 * A140459 A140460 A140461

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 26 2008

Extensions

More terms from Harvey P. Dale, Nov 12 2011

Status

approved