A329243 a(n) = Pi(8,3)(prime(n)) + Pi(8,5)(prime(n)) + Pi(8,7)(prime(n)) - 3*Pi(8,1)(prime(n)), where Pi(a,b)(x) denotes the number of primes in the arithmetic progression a*k + b less than or equal to x.

0, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 9, 10, 11, 8, 9, 10, 7, 4, 5, 6, 7, 8, 5, 6, 7, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 16, 17, 14, 15, 12, 13, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 12, 13, 14, 11, 12, 13, 10, 11, 12, 13, 14, 15, 16

Offset

1,3

Comments

The initial terms are nonnegative integers, a(n) is negative for some prime(n) ~ 10^28.127. See the comments about "Chebyshev's bias" in A329242.

Links

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

Example

For prime(25) = 97, there are 5 primes <= 97 that are congruent to 1 mod 8 (17, 41, 73, 89, 97), 7 primes congruent to 3 mod 8 (3, 11, 19, 43, 59, 67, 83), 6 primes congruent to 5 mod 8 (5, 13, 29, 37, 53, 61), 6 primes congruent to 7 mod 8 (7, 23, 31, 47, 71, 79), so a(25) = 7 + 6 + 6 - 3*5 = 4.

Prog

(PARI) a(n) = my(k=0); forprime(p=3, prime(n), if(p%8==1, k-=3, k++)); k

Crossrefs

Cf. A329242.

Cf. A321856, A066520, A321857, A321859, A321860.

Sequence in context: A070772 A094937 A215089 * A161768 A213925 A141810

Adjacent sequences: A329240 A329241 A329242 * A329244 A329245 A329246

Keyword

sign

Author

Jianing Song, Nov 08 2019

Extensions

Edited by Peter Munn, Nov 19 2023

Status

approved