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%I #30 Aug 10 2023 03:02:30
%S 0,17,539,652,6420,350857847
%N Integers k such that A007504(k) + 1 is a square.
%C Integers k such that the sum of the first k primes + 1 is a square.
%C Integers k such that A014284(k+1) is a square.
%C In A110996, it is commented that a(6) > 250000, if it exists.
%C a(6) > 50000000, if it exists. - _Jon E. Schoenfield_, Nov 29 2015
%e a(2) = 17 because A007504(17) + 1 = 440 + 1 = 441 is a square.
%t t = Accumulate[Prime@ Range@ 100000]; Prepend[Select[Range@ 7000, IntegerQ@ Sqrt[t[[#]] + 1] &], 0] (* _Michael De Vlieger_, Nov 29 2015, after _Zak Seidov_ at A007504 *)
%t Join[{0},Position[Accumulate[Prime[Range[6500]]]+1,_?(IntegerQ[Sqrt[ #]]&)]] // Flatten (* _Harvey P. Dale_, Feb 12 2018 *)
%o (PARI) lista(nn) = { print1(0, ", "); s = 1; for(k=1, nn, s += prime(k); if(issquare(s), print1(k, ", ")););}
%Y Cf. A007504, A014284, A033997, A089228, A110996.
%K nonn,more
%O 1,2
%A _Altug Alkan_, Nov 26 2015
%E a(6) from _Jinyuan Wang_, Aug 09 2023
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