A066049 Numbers n such that 2*n^2 - 1 is a prime.

2, 3, 4, 6, 7, 8, 10, 11, 13, 15, 17, 18, 21, 22, 24, 25, 28, 34, 36, 38, 39, 41, 42, 43, 45, 46, 49, 50, 52, 56, 59, 62, 63, 64, 69, 73, 76, 80, 81, 85, 87, 91, 92, 95, 98, 102, 108, 109, 112, 113, 115, 118, 125, 126, 127, 132, 134, 137, 140, 141, 143, 153, 154, 155

Offset: 1

Author

N. J. A. Sloane, Jan 09 2002

Keywords

• nonn

Comments

It is conjectured that this sequence is infinite.

A066436 gives resulting primes p such that (p+1)/2 is square. - Ray Chandler

References

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

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A028870, A066436, A090697, A091176, A110558.

Programs

Mathematica

Select[Range[200],PrimeQ[2#^2-1]&] (* Harvey P. Dale, Jun 14 2011 *)

PARI

{ n=0; for (m=1, 10^9, if (isprime(2*m^2 - 1), write("b066049.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 08 2009

Formula

a(n) = A090697(n)/2 = A110558(n)/4. - Ray Chandler, Sep 15 2005

a(n) = A160697(n+1). - Reinhard Zumkeller, May 24 2009

Extensions

Extended by Ray Chandler, Sep 15 2005