A066436 Primes of the form 2*n^2 - 1.

7, 17, 31, 71, 97, 127, 199, 241, 337, 449, 577, 647, 881, 967, 1151, 1249, 1567, 2311, 2591, 2887, 3041, 3361, 3527, 3697, 4049, 4231, 4801, 4999, 5407, 6271, 6961, 7687, 7937, 8191, 9521, 10657, 11551, 12799, 13121, 14449, 15137, 16561

Offset

1,1

Comments

It is conjectured that this sequence is infinite.

Also primes p such that 8p + 8 is a square. - Cino Hilliard, Dec 18 2003

Also primes p such that 2p+2 is square; also primes p such that (p+1)/2 is square. - Ray Chandler, Sep 15 2005

Arithmetic numbers which are squares, A003601(p)=A000290(k), p prime, k integer. sigma_1(p)/sigma_0(p)=k^2; p prime, k integer. - Ctibor O. Zizka, Jul 14 2008

References

D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Project Euler, Problem 216: Investigating the primality of numbers of the form 2n^2-1.

Mathematica

Select[2*Range[200]^2-1, PrimeQ] (* Harvey P. Dale, Aug 29 2016 *)

Prog

(Magma) [ p: n in [1..100] | IsPrime(p) where p is 2*n^2-1 ]; // Klaus Brockhaus, Dec 29 2008
(PARI) { n=0; for (m=1, 10^9, p=2*m^2 - 1; if (isprime(p), write("b066436.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 14 2010

Crossrefs

See A066049 for the values of n, see A091176 for prime index.

Cf. A090697, A110558, A003601, A000290.

Sequence in context: A178491 A319304 A144861 * A128002 A301695 A301725

Adjacent sequences: A066433 A066434 A066435 * A066437 A066438 A066439

Keyword

nonn

Author

N. J. A. Sloane, Jan 09 2002

Status

approved