1,1

Then 2p+1 is called a safe prime: see A005385.

Primes such that the equation phi(k) = 2p has solutions, where phi is the totient function. See A087634 for another such collection of primes. - T. D. Noe (noe(AT)sspectra.com), Oct 24 2003

Subsequence of A117360. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Mar 10 2006

Let q = 2n+1. For these n (and q), the difference of two cyclotomic polynomials can be written as a cyclotomic polynomial in x^2: Phi(q,x) - Phi(2q,x) = 2x Phi(n,x^2). - T. D. Noe (noe(AT)sspectra.com), Jan 04 2008

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.

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 83.

T. D. Noe, Table of n, a(n) for n = 1..10000

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

C. K. Caldwell, The Prime Glossary, Sophie Germain Prime

H. Lifchitz, A new and simpler primality test for Sophie-Germain numbers(q=2*p+1)

T. Tao, Obstructions to uniformity, and arithmetic patterns in the primes

Vmoraru, PlanetMath.org, Germain prime

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Wikipedia, Sophie Germain prime

L. Riddle, Sophie Germain and Fermat's Last Theorem

A:={}: for n from 1 to 246 do if isprime(2*ithprime(n)+1)=true then A:=A union {ithprime(n)} else A:=A fi od: A:=A; - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 09 2004

Select[Prime[Range[1000]], PrimeQ[2#+1]&]

Cf. A005385, A007700, A023272, A023302, A023330, A057331, A005602.

Cf. A087634.

Sequence in context: A118332 A118333 A131101 this_sequence A118571 A118504 A038905

Adjacent sequences: A005381 A005382 A005383 this_sequence A005385 A005386 A005387

nonn,nice

njas