A340764 Number of primes p <= n that are congruent to 2 modulo 3.

0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13

Offset: 1

Author

Jianing Song, Apr 28 2021

Keywords

• nonn
• easy

Examples

			There are 13 primes <= 100 that are congruent to 2 modulo 3, namely 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, so a(100) = 13.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003627, A340763, A340767, A066339, A066490.

Programs

Mathematica

Accumulate[Table[If[PrimeQ[n]&&Mod[n,3]==2,1,0],{n,90}]] (* Harvey P. Dale, May 12 2022 *)

PARI

a(n) = sum(i=1, n, isprime(i) && (i%3==2))

Formula

A340763(n) + a(n) = A000720(n) - 1 for n >= 3.