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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 09 2002
STATUS
approved