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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 n-th 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = 2*n - pi(2*p_n).
a(n) = 2*n - A020900(n). - Michel Marcus, Sep 11 2020
a(n) = 1 + A331677(n). - Alois P. Heinz, Oct 09 2020
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
Sequence in context: A096036 A108504 A036468 * A345380 A367128 A028829
KEYWORD
nonn
AUTHOR
Ya-Ping Lu, Sep 11 2020
STATUS
approved

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Last modified March 4 12:21 EST 2024. Contains 370532 sequences. (Running on oeis4.)