A230327 - OEIS

%I #9 Oct 18 2013 12:24:29

%S 7,6,3,42,107,6,38,1,1631,170,38,119,5,546,78,309,85,604,199,57,270,2,

%T 3,333,45,2,178,1708,291,2,35,72,322,19,84,5,155,346,122,2175,1395,24,

%U 886,2,3108,168,14,499,340,294,156,578,325,240,115,61,283,1035

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

%e a(2)=7 because 17+19 (2 terms) = 36 is a square, 17 being the 7th prime.

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

%o (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

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

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

%K nonn

%O 2,1

%A _Michel Marcus_, Oct 16 2013