A264858 Integers k such that A007504(k) + 1 is a square.

0, 17, 539, 652, 6420, 350857847

Offset: 1

Author

Altug Alkan, Nov 26 2015

Keywords

• nonn
• more

Comments

Integers k such that the sum of the first k primes + 1 is a square.

Integers k such that A014284(k+1) is a square.

In A110996, it is commented that a(6) > 250000, if it exists.

a(6) > 50000000, if it exists. - Jon E. Schoenfield, Nov 29 2015

Examples

			a(2) = 17 because A007504(17) + 1 = 440 + 1 = 441 is a square.
		

Crossrefs

Cf. A007504, A014284, A033997, A089228, A110996.

Programs

Mathematica

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 *)
Join[{0},Position[Accumulate[Prime[Range[6500]]]+1,?(IntegerQ[Sqrt[ #]]&)]] // Flatten (* _Harvey P. Dale, Feb 12 2018 *)

PARI

lista(nn) = { print1(0, ", "); s = 1; for(k=1, nn, s += prime(k); if(issquare(s), print1(k, ", ")););}

Extensions

a(6) from Jinyuan Wang, Aug 09 2023