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A166261 Numbers n with property that sum of 120 successive primes starting with n-th prime is a square. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum(prime(k),k=n,n+119)=s^2; corresponding values of s: 3734, 3846, 8660, 10602, 13248, 13690, 14318, 14936, 17934, 20458 (A166262).

LINKS

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

EXAMPLE

a(1)=10917: sum[Prime[i], {i,10917,10917+119}]=3734^2=(A166262(1))^2,

a(2)=11527: sum[Prime[i], {i,11527,11527+119}]=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

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

AUTHOR

Zak Seidov, Oct 10 2009

EXTENSIONS

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

STATUS

approved

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Last modified October 16 06:19 EDT 2019. Contains 328048 sequences. (Running on oeis4.)