%I #8 Sep 14 2017 03:53:27
%S 1,3,6,12,30,54,60,72,120,126,144,174,198,210,294,300,318,354,408,420,
%T 426,432,480,498,522,564,588,594,600,624,630,648,666,714,720,852,864,
%U 978,1002,1050,1056,1080,1098,1122,1146,1152,1170,1176,1200,1206,1458
%N a(n) is the smallest number > a(n1) such that 1 + a(1)^2 + a(2)^2 + ... + a(n)^2 is a prime.
%C The corresponding primes are 2, 11, 47, 191, 1091, 4007, 7607, 12791, 27191, 43067, ...
%e a(1) = 1 because 1 + 1^2 = 2 is prime;
%e a(2) = 3 because 1 + 1^2 + 2^2 = 6 is not prime, but 1 + 1^2 + 3^2 = 11 is prime;
%e a(3) = 6 because neither 1 + 1^2 + 3^2 + 4^2 = 27 nor 1 + 1^2 + 3^2 + 5^2 = 36 is prime, but 1 + 1^2 + 3^2 + 6^2 = 47 is prime.
%t p=1;lst={p};Do[If[PrimeQ[p+n^2],AppendTo[lst,n];p=p+n^2],{n,1,1500}];lst
%Y Cf. A051935.
%K nonn
%O 1,2
%A _Michel Lagneau_, Nov 24 2012
