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A066049
Numbers n such that 2*n^2 - 1 is a prime.
31
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
1,1
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.
FORMULA
a(n) = A090697(n)/2 = A110558(n)/4. - Ray Chandler, Sep 15 2005
a(n) = A160697(n+1). - Reinhard Zumkeller, May 24 2009
MATHEMATICA
Select[Range[200], PrimeQ[2#^2-1]&] (* Harvey P. Dale, Jun 14 2011 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 09 2002
EXTENSIONS
Extended by Ray Chandler, Sep 15 2005
STATUS
approved