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

1,13

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A126235 A220104 A191228 * A286103 A056556 A111651

Adjacent sequences: A340760 A340761 A340762 * A340764 A340765 A340766

Keyword

nonn,easy

Author

Jianing Song, Apr 28 2021

Status

approved