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

3, 17, 577, 665857

Offset

1,1

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

Links

Table of n, a(n) for n=1..4.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. A000290, A002315, A257553.

Sequence in context: A257116 A305375 A128300 * A001601 A061119 A094133

Adjacent sequences: A292079 A292080 A292081 * A292083 A292084 A292085

Keyword

nonn,fini,full

Author

Jaroslav Krizek, Sep 12 2017

Status

approved