A166261 Numbers k with property that the sum of 120 successive primes starting with prime(k) is a square.

10917, 11527, 50923, 73894, 111468, 118436, 128662, 139123, 195234, 249281, 332863, 435489, 438080, 482557, 538373, 542299, 650254, 679958, 722145, 803501, 810871, 820409, 962582, 970711, 1003544, 1027732, 1030010, 1190134, 1204929, 1305603, 1636065, 1689410

Offset

1,1

Comments

Corresponding values of s = sqrt(Sum_{i=k..k+119} prime(i)) are A166262.

Links

Table of n, a(n) for n=1..32.

Example

a(1) = 10917: Sum_{i=0..119} prime(10917+i) = 3734^2 = A166262(1)^2,
a(2) = 11527: Sum_{i=0..119} prime(11527+i) = 3846^2 = A166262(2)^2.

Mathematica

PrimePi/@Select[Partition[Prime[Range[169*10^4]], 120, 1], IntegerQ[ Sqrt[ Total[ #]]]&][[All, 1]] (* Harvey P. Dale, Jan 22 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(i, ", ")); ); } \\ Michel Marcus, Oct 15 2013
(PARI) S=vecsum(primes(119)); p=0; q=prime(120); for(n=1, oo, issquare(S+=q-p) && print1(n", "); q=nextprime(q+1); p=nextprime(p+1))} \\ It is about 25% faster to avoid "nextprime(p)" at expense of keeping the last 120 primes used in a vector p, using {my(i=Mod(0, 120)); ...p[lift(i)+1]... i++}. - M. F. Hasler, Jan 04 2020

Crossrefs

Cf. A166262.

Cf. A064397 (2 primes), A076305 (3 primes), A072849 (4 primes), A166255 (70 primes).

Sequence in context: A082710 A240604 A065322 * A089381 A092007 A043581

Adjacent sequences: A166258 A166259 A166260 * A166262 A166263 A166264

Keyword

nonn,less

Author

Zak Seidov, Oct 10 2009

Extensions

a(30)-a(32) from Michel Marcus, Oct 15 2013

Edited by M. F. Hasler, Jan 04 2020

Status

approved