A340764 - OEIS

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

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OFFSET

1,5

LINKS

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

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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

PROG