1,1

Primes p such that 2 is a quadratic residue mod p.

Also primes p such that p divides 2^(p-1)/2 - 1. - Cino Hilliard (hillcino368(AT)gmail.com), Sep 04 2004

A001132 is exactly formed by the prime numbers of A118905 : in fact at first every prime p of A118905 is p=u^2-v^2+2uv, with for example u odd and v even so that : p-1=4u'(u'+1)-4v'(2u'+1-v') when u=2u'+1 and v=2v'. u'(u'+1) is even and v'(2u'+1-v') is always even. At second hand if p=8k+-1, p has the shape x^2-2y^2 ; letting u=x-y and v=y, comes p=(x-y)^2-y^2+2(x-y)y=u^2-v^2+2uv so p is a sum of the two legs of a pythagorean triangle. [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 16 2008]

Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)

These are also the primes of form x^2-2y^2, excluding 2. See A141131.

(End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

T. D. Noe, Table of n, a(n) for n=1..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Index entries for related sequences

C. Banderier, Calcul de (2/p)

For primes p such that x^m = 2 (mod p) has a solution see A001132 (for m=2), A040028 (m=3), A040098 (m=4), A040159 (m=5), A040992 (m=6), A042966 (m=7), A045315 (m=8), A049596 (m=9), A049542 (m=10) - A049595 (m=63). Jeff Lagarias (lagarias(AT)umich.edu) points out that all these sequences are different, although this may not be apparent from looking just at the initial terms.

Agrees with A038873 except for initial term.

A118905 [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 16 2008]

Sequence in context: A107643 A058529 A120681 this_sequence A165353 A048976 A088546

Adjacent sequences: A001129 A001130 A001131 this_sequence A001133 A001134 A001135

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).