A166262 Numbers n with property that n^2 is a sum of some 120 successive primes.

3734, 3846, 8660, 10602, 13248, 13690, 14318, 14936, 17934, 20458, 23902, 27614, 27704, 29176, 30942, 31064, 34238, 35070, 36216, 38346, 38532, 38774, 42236, 42428, 43190, 43742, 43794, 47308, 47622, 49708, 56070, 57036, 58856, 65692, 66122, 66940, 68016

Offset: 1

Author

Zak Seidov, Oct 10 2009

Keywords

• nonn

Comments

n^2=sum(prime(k),k=m,m+119); corresponding values of m: 10917, 11527, 50923, 73894, 111468, 118436, 128662, 139123, 195234 (A166261).

Examples

			a(1)=3734: 3734^2=sum[Prime[i], {i,10917,10917+119}],
a(2)=3846: 3846^2=sum[Prime[i], {i,11527,11527+119}].
		

Crossrefs

Cf. A166261.

Programs

Mathematica

Select[Sqrt[#]&/@(Total/@Partition[Prime[Range[5*10^6]],120,1]),IntegerQ] (* Harvey P. Dale, Jul 17 2019 *)

PARI

lista(nn) = {pr = primes(nn); for (i=1, nn-119, s = sum(k=i, i+119, pr[k]); if (issquare(s), print1(sqrtint(s), ", ")););} \\ Michel Marcus, Oct 15 2013

Extensions

a(35)-a(37) from Michel Marcus, Oct 15 2013