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

1,1

Comments

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

Links

Table of n, a(n) for n=1..37.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A166261.

Sequence in context: A251206 A038012 A020410 * A340403 A235977 A235243

Adjacent sequences: A166259 A166260 A166261 * A166263 A166264 A166265

Keyword

nonn

Author

Zak Seidov, Oct 10 2009

Extensions

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

Status

approved