login
A292082
Primes p such that (p^2 - 1) / 2 is a square (A000290).
0
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
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).
Sequence in context: A257116 A305375 A128300 * A001601 A061119 A094133
KEYWORD
nonn,fini,full
AUTHOR
Jaroslav Krizek, Sep 12 2017
STATUS
approved