

A334051


The difference between the number of prime numbers in the ranges (1, p_n] and (p_n, 2*p_n], where p_n is the nth prime.


1



0, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 3, 4, 5, 6, 5, 4, 6, 6, 6, 8, 7, 8, 8, 6, 6, 8, 9, 11, 12, 8, 9, 8, 9, 8, 10, 9, 10, 11, 12, 11, 12, 11, 12, 13, 14, 12, 10, 11, 12, 12, 13, 14, 13, 13, 13, 15, 16, 17, 18, 19, 18, 14, 14, 16, 17, 13, 14, 13, 15, 16, 17, 16, 16
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OFFSET

1,3


LINKS



FORMULA

a(n) = 2*n  pi(2*p_n).


EXAMPLE

a(6) = 2*6  pi(2*p_6) = 12  pi(2*13) = 12  pi(26) = 12  9 = 3.


PROG

(Python)
from sympy import prime, primepi
for n in range(1, 10001):
a = 2*n  primepi(2*prime(n))
print(a)
(PARI) a(n) = 2*n  primepi(2*prime(n)); \\ Michel Marcus, Sep 11 2020


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



