A133204 Primes p such that the non-Pellian equation x^2-2py^2=-1 is solvable.

5, 13, 29, 37, 41, 53, 61, 101, 109, 113, 137, 149, 157, 173, 181, 197, 229, 269, 277, 293, 313, 317, 349, 373, 389, 397, 409, 421, 457, 461, 509, 521, 541, 557, 569, 613, 653, 661, 677, 701, 709, 733, 757, 761, 773, 797, 809, 821, 829, 853, 857, 877, 941

Offset

1,1

Comments

The sequence contains no primes congruent to 3 modulo 4 and all primes congruent to 5 modulo 8.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

H. von Lienen, The quadratic form x^2-2py^2, J. Number Theory 10 (1978), 10-15.

Mathematica

fQ[n_] := Solve[x^2 + 1 == 2 n*y^2, {x, y}, Integers] != {}; Select[ Prime@ Range@ 160, fQ] (* Robert G. Wilson v, Dec 19 2013 *)

Crossrefs

Sequence in context: A178854 A224339 A368546 * A207040 A309588 A268614

Adjacent sequences: A133201 A133202 A133203 * A133205 A133206 A133207

Keyword

nonn

Author

David Brink, Dec 29 2007

Status

approved