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

1,1

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

Links

Table of n, a(n) for n=1..13.

Example

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.

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 *)

Crossrefs

Cf. A000290, A001601, A088165, A256944.

Sequence in context: A051291 A178178 A333499 * A143013 A113483 A173868

Adjacent sequences: A257550 A257551 A257552 * A257554 A257555 A257556

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 29 2015

Extensions

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

Edited by Wolfdieter Lang, May 07 2015

Status

approved