A338521 The number of primes between n-primepi(n) and n.

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

Offset

1,8

Comments

There is at least one prime number between n-primepi(n) and n, or a(n) >= 1, for n >= 3 (see Corollary 3 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 - 1) - primepi(n - primepi(n)).

a(n) = A000720(n - 1) - A000720(n - A000720(n)).

a(n) = A000720(n -1) - A000720(A062298(n)).

Mathematica

Array[Subtract @@ Map[PrimePi, {#1 - 1, #1 - #2}] & @@ {#, PrimePi[#]} &, 105] (* Michael De Vlieger, Nov 05 2020 *)

Prog

(Python)
from sympy import primepi
for n in range(1, 101):
    pi = primepi(n)
    pi_1 = primepi(n - 1)
    a = pi_1 - primepi(n - pi)
    print(a)
(PARI) a(n) = primepi(n - 1) - primepi(n - primepi(n)); \\ Michel Marcus, Nov 01 2020

Crossrefs

Cf. A000720, A062298, A337788.

Sequence in context: A352085 A036541 A176505 * A036225 A236859 A278401

Adjacent sequences: A338518 A338519 A338520 * A338522 A338523 A338524

Keyword

nonn

Author

Ya-Ping Lu, Nov 01 2020

Status

approved