A340763 Number of primes p <= n that are congruent to 1 modulo 3.

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 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, 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

Offset: 1

Author

Jianing Song, Apr 28 2021

Keywords

• nonn
• easy

Examples

			There are 11 primes <= 100 that are congruent to 1 modulo 3, namely 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, so a(100) = 11.
		

Links

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

Crossrefs

Cf. A002476, A340764, A172104, A066339, A066490.

Programs

PARI

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

Formula

a(n) + A340764(n) = A000720(n) - 1 for n >= 3.