A156876 Number of primes <= n that are safe primes or Sophie Germain primes.

0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12

Offset: 1

Author

Reinhard Zumkeller, Feb 18 2009

Keywords

• nonn

Examples

			a(120) = #{2,3,5,7,11,23,29,41,47,53,59,83,89,107,113} = 15.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A156658, A005384, A005385, A000720.

Cf. A156874, A156875, A156877, A156878.

Programs

Mathematica

Accumulate[Table[If[AllTrue[{n,2n+1},PrimeQ]||AllTrue[{n,(n-1)/2}, PrimeQ],1,0],{n,100}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 24 2019 *)

PARI

a(n) = my(nb=0); forprime(p=2, n, if (isprime(2*p+1) || isprime((p-1)/2), nb++)); nb; \\ Michel Marcus, Nov 06 2022

Formula

a(n) = A156874(n)+A156875(n)-A156877(n) = A000720(n)-A156878(n).