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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A156658, A005384, A005385, A000720.

Cf. A156874, A156875, A156877, A156878.

Sequence in context: A094235 A328003 A262558 * A137397 A239684 A062571

Adjacent sequences: A156873 A156874 A156875 * A156877 A156878 A156879

Keyword

nonn

Author

Reinhard Zumkeller, Feb 18 2009

Status

approved