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 A066436 Primes of the form 2*n^2 - 1. 48
 7, 17, 31, 71, 97, 127, 199, 241, 337, 449, 577, 647, 881, 967, 1151, 1249, 1567, 2311, 2591, 2887, 3041, 3361, 3527, 3697, 4049, 4231, 4801, 4999, 5407, 6271, 6961, 7687, 7937, 8191, 9521, 10657, 11551, 12799, 13121, 14449, 15137, 16561 (list; graph; refs; listen; history; text; internal format)
 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 Project Euler, Problem 216: Investigating the primality of numbers of the form 2n^2-1. 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 See A066049 for the values of n, see A091176 for prime index. Cf. A090697, A110558, A003601, A000290. Sequence in context: A178491 A319304 A144861 * A128002 A301695 A301725 Adjacent sequences: A066433 A066434 A066435 * A066437 A066438 A066439 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 09 2002 STATUS approved

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Last modified November 30 01:30 EST 2023. Contains 367452 sequences. (Running on oeis4.)