A230327 Index of smallest prime such that the sum of n consecutive primes starting with this specific prime is a square.

7, 6, 3, 42, 107, 6, 38, 1, 1631, 170, 38, 119, 5, 546, 78, 309, 85, 604, 199, 57, 270, 2, 3, 333, 45, 2, 178, 1708, 291, 2, 35, 72, 322, 19, 84, 5, 155, 346, 122, 2175, 1395, 24, 886, 2, 3108, 168, 14, 499, 340, 294, 156, 578, 325, 240, 115, 61, 283, 1035

Offset

2,1

Links

Table of n, a(n) for n=2..59.

Example

a(2)=7 because 17+19 (2 terms) = 36 is a square, 17 being the 7th prime.
a(3)=6 because 13+17+19 (3 terms) =49 is a square, 13 being the 6th prime.

Prog

(PARI) a(n, lim=10^5) = {n --; pr = primes(lim); for (i = 1, lim-n, s = sum(k=i, i+n, pr[k]); if (issquare(s), return (i)); ); return (0); } \\ Michel Marcus, Oct 16 2013

Crossrefs

Cf. A064397 (2 primes), A076305 (3 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes).

Cf. A132955 (primes themselves), A132956 (squares=sums), A132957 (square roots of sums).

Sequence in context: A187799 A288935 A132714 * A105419 A288242 A289266

Adjacent sequences: A230324 A230325 A230326 * A230328 A230329 A230330

Keyword

nonn

Author

Michel Marcus, Oct 16 2013

Status

approved