Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #48 Sep 08 2022 08:45:04
%S 7,17,31,71,97,127,199,241,337,449,577,647,881,967,1151,1249,1567,
%T 2311,2591,2887,3041,3361,3527,3697,4049,4231,4801,4999,5407,6271,
%U 6961,7687,7937,8191,9521,10657,11551,12799,13121,14449,15137,16561
%N Primes of the form 2*n^2 - 1.
%C It is conjectured that this sequence is infinite.
%C Also primes p such that 8p + 8 is a square. - _Cino Hilliard_, Dec 18 2003
%C Also primes p such that 2p+2 is square; also primes p such that (p+1)/2 is square. - _Ray Chandler_, Sep 15 2005
%C 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
%D D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 31.
%H Harry J. Smith, <a href="/A066436/b066436.txt">Table of n, a(n) for n = 1..1000</a>
%H Project Euler, <a href="https://projecteuler.net/problem=216">Problem 216: Investigating the primality of numbers of the form 2n^2-1</a>.
%t Select[2*Range[200]^2-1,PrimeQ] (* _Harvey P. Dale_, Aug 29 2016 *)
%o (Magma) [ p: n in [1..100] | IsPrime(p) where p is 2*n^2-1 ]; // _Klaus Brockhaus_, Dec 29 2008
%o (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
%Y See A066049 for the values of n, see A091176 for prime index.
%Y Cf. A090697, A110558, A003601, A000290.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jan 09 2002