A337788 The number of primes between n exclusive and n+primepi(n) inclusive.

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

Offset

1,9

Comments

There is at least one prime number in the range of (n, n + primepi(n)], or a(n) >= 1, for n >= 2 (see Corollary 1 in the paper by Ya-Ping Lu attached in the links).

Links

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

Ya-Ping Lu, Lower Bounds for the Number of Primes in Some Integer Intervals

Formula

a(n) = primepi(n + primepi(n)) - primepi(n)

a(n) = A000720(n + A000720(n)) - A000720(n)

a(n) = A000720(A095117(n)) - A000720(n)

Prog

(Python)
from sympy import primepi
for n in range(1, 101):
    pi = primepi(n)
    a = primepi(n + pi) - pi
    print(a)
(PARI) a(n) = primepi(n+primepi(n)) - primepi(n); \\ Michel Marcus, Oct 27 2020

Crossrefs

Cf. A000720, A095117.

Sequence in context: A271824 A253589 A332992 * A346510 A023568 A081753

Adjacent sequences: A337785 A337786 A337787 * A337789 A337790 A337791

Keyword

nonn

Author

Ya-Ping Lu, Oct 27 2020

Status

approved