A066436 - 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