A335660 a(n) = n - A334714(n).

0, 0, 0, 1, 1, 1, 1, 1, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 4, 3, 3, 3, 4, 5, 5, 5, 5, 5, 4, 4, 3, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 3, 3, 4, 5, 5, 5, 5, 5, 4, 4, 3, 2, 2, 3, 4, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7

Offset

1,9

Comments

a(n) >= 2 for n >= 9. (See Theorem 1.1. in Alkan, Booker & Luca.)

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Altug Alkan, Andrew R. Booker, and Florian Luca, On a recursively defined sequence involving the prime counting function, arXiv:2006.08013 [math.NT], 2020.

Formula

a(n) = n - Sum_{k=1..n} A335294(n).

Mathematica

f[1] = 1; f[n_] := f[n] = PrimePi[n] - PrimePi[Sum[f[k], {k, 1, n - 1}]]; m = 100 ; Range[m] - Accumulate @ Array[f, m] (* Amiram Eldar, May 03 2021 *)

Crossrefs

Cf. A000720, A334714, A335294, A335662.

Sequence in context: A031283 A293229 A185437 * A210681 A366544 A096520

Adjacent sequences: A335657 A335658 A335659 * A335661 A335662 A335663

Keyword

nonn,look

Author

Seiichi Manyama, Jun 17 2020

Status

approved