A334614 a(n) = pi(prime(n) - n) + n, where pi is the prime counting function.

1, 2, 4, 6, 8, 10, 11, 13, 15, 18, 19, 21, 22, 24, 26, 28, 30, 32, 34, 35, 36, 38, 40, 42, 45, 47, 48, 50, 51, 53, 55, 57, 60, 61, 65, 66, 67, 68, 70, 72, 74, 76, 77, 79, 81, 82, 85, 88, 89, 91, 93, 94, 95, 99, 101, 102, 104, 105, 106, 107, 108, 112, 116, 117

Offset

1,2

Comments

It can be shown that a(n) > a(n-1) >= 1 and a(n) <= 2*n - 1 < 2*n (see proofs in the Links section).

Links

Table of n, a(n) for n=1..64.

Ya-Ping Lu, Proofs of the two observations in the Comments section

Formula

a(n) = A000720(A014689(n)) + n.

a(n) = A065328(n) + n. - Michel Marcus, Sep 12 2020

Mathematica

Table[PrimePi[Prime[n] - n] + n, {n, 1, 64}] (* Amiram Eldar, Sep 09 2020 *)

Prog

(Python)
from sympy import prime, primepi
for n in range(1, 100001):
    a_n = primepi(prime(n) - n) + n
    print(a_n)
(PARI) a(n) = n + primepi(prime(n) - n); \\ Michel Marcus, Sep 09 2020

Crossrefs

Cf. A000040, A000720, A014688, A014689, A062298, A065328, A097933.

Cf. A332086, A337334.

Sequence in context: A050420 A214671 A291171 * A185449 A096922 A241071

Adjacent sequences: A334611 A334612 A334613 * A334615 A334616 A334617

Keyword

nonn

Author

Ya-Ping Lu, Sep 08 2020

Status

approved