A257553 Primes whose squares are not the sums of two consecutive nonsquares.

2, 3, 7, 17, 41, 239, 577, 665857, 9369319, 63018038201, 489133282872437279, 19175002942688032928599, 123426017006182806728593424683999798008235734137469123231828679

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 29 2015

Keywords

• nonn

Comments

Primes of the form A257282(k).

2 is in this sequence, and an odd prime p is in the sequence iff either (p^2 - 1)/2 or (p^2 + 1)/2 is a square. - Wolfdieter Lang, May 07 2015

According to the Neretin comment in A257282, and as the primes of A001333 are in A086395, this is (apart from the 2) the same as A086395. - R. J. Mathar, Jan 31 2024

Examples

			2 is in the sequence because it is prime and its square 4 is in A256944: 4 is not a sum of consecutive numbers.
3 is in the sequence because it is prime and its square 9 is in A256944: 9 = 2^2 + 5.
7 is in the sequence because it is prime and its square 49 is in A256944: 49 = 24 + 5^2.
5 is not in the sequence because neither 12 nor 13 is a square.
		

Crossrefs

Cf. A000290, A001601, A088165, A256944.

Programs

Mathematica

lim = 1000000; s = Plus @@@ (Partition[#, 2, 1] & @ Complement[Range@ lim, Range[Floor@ Sqrt[lim]]^2]); Select[Sqrt[#] & /@ Select[Range@ Floor[Sqrt[lim]]^2, ! MemberQ[s, #] &] , PrimeQ] (* Michael De Vlieger, Apr 29 2015 *)

Extensions

Name clarified by Michael De Vlieger and Jon E. Schoenfield, May 03 2015

Edited by Wolfdieter Lang, May 07 2015