A379731 List of y coordinates of prime numbers in the Cartesian grid defined in A379643.

0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 4, 4, 3, 3, 3, 2, 1, 2, 2, 2, 3, 2, 2, 2, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 4, 5, 5, 5, 5, 5, 6, 5, 5, 4, 4, 3, 3, 4, 4, 5, 4, 4, 5, 5, 5, 4, 5, 5, 4, 4, 5, 4, 4, 4, 5, 5, 5, 6, 7, 6, 5, 5, 6, 6, 5, 5, 5, 4

Offset

1,6

Comments

The corresponding x coordinates are given in A379643. Positions of the first 1 miilion primes are illustrated in Links in A379643.

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = pi_{8,5}(p_n) - pi_{8,1}(p_n), where pi_{m,b}(x) is the number of primes <= x which are congruent to b (mod m) and p_n the n-th prime.

Prog

(Python)
from sympy import nextprime; R = [0, 0]; y, p = 0, 3
for _ in range(85):
    p = nextprime(p); d = (p%8 - 3)//2
    if d in {-1, 1}: y += d
    R.append(y)
print(*R, sep = ', ')

Crossrefs

Cf. A297448, A345293, A379643.

Sequence in context: A240837 A369376 A060502 * A035439 A059111 A103502

Adjacent sequences: A379728 A379729 A379730 * A379732 A379733 A379734

Keyword

sign

Author

Ya-Ping Lu, Dec 31 2024

Status

approved