A292082 Primes p such that (p^2 - 1) / 2 is a square (A000290).

3, 17, 577, 665857

Offset: 1

Author

Jaroslav Krizek, Sep 12 2017

Keywords

• nonn
• fini
• full

Comments

Corresponding values of squares: 4, 144, 166464, 221682772224.

Subsequence of A257553.

Conjecture: sequence is finite.

Numbers k such that (k^2 - 1) / 2 is a square are given by A001541, of which the only prime terms are 3, 17, 577, and 665857 (see Alexander Adamchuk's Nov 24 2006 Comments entry there), so a(4) = 665857 is the last term of this sequence. - Jon E. Schoenfield, Nov 20 2017

Examples

			Number 3 is in the sequence because (3^2 - 1) / 2 = 4 (square).
		

Crossrefs

Cf. A088165 (primes p such that (p^2 + 1) / 2 is a square).

Cf. A000290, A002315, A257553.

Programs

Magma

[n: n in [3..1000000] | IsPrime(n) and IsSquare((n^2-1) / 2)];

Mathematica

Select[Prime[Range[55000]],IntegerQ[Sqrt[(#^2-1)/2]]&] (* Harvey P. Dale, Mar 10 2019 *)