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

1,5

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

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

Crossrefs

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

Sequence in context: A138194 A133876 A321018 * A152467 A242602 A097992

Adjacent sequences: A340761 A340762 A340763 * A340765 A340766 A340767

Keyword

nonn,easy

Author

Jianing Song, Apr 28 2021

Status

approved