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%I #7 Jul 22 2012 17:19:29
%S 7,5,7,5,7,5,151,29,31,5,7,101,35,25,7,5,7,5,7,5,35,53,7,25,35,25,43,
%T 5,35,65,7,65,91,17,7,65,83,13,59,173,7,25,11,13,7,17,7,25,11,17,7,65,
%U 43,61,35,17,79,53,23,29,11,29,35,101,7,17,11,29,35,5,35,25,35
%N Arithmetic mean of next a(n) successive squares is prime.
%C Corresponding primes (and arithmetic means):
%C 13, 83, 229, 443, 733, 1091, 14221, 40471, 53441, 62003, 65029, 96331, 142231, 165701, 178933, 184043, 189229, 194483, 199813, 205211, 223831, 267523, 299213, 317021, 351751, 388181, 431803, 463763, 491503, 564353, 619373
%C Conjecture: for some k and x, a(n)=A214451(n+x) for n>k.
%e (0+1+4+9+16+25+36)/7 = 13, so a(1)=7. The next set of successive squares with prime arithmetic mean: (7^2 + 8^2 + 9^2 +100 + 11^2)/5 = 83, so a(2)=5.
%Y Cf. A000040, A000290, A214442, A214451.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, Jul 18 2012