A321211 - OEIS

A321211

Let S be the sequence of integer sets defined by these rules: S(1) = {1}, and for any n > 1, S(n) = {n} U S(pi(n)) U S(n - pi(n)) (where X U Y denotes the union of the sets X and Y and pi is the prime counting function); a(n) = the number of elements of S(n).

1, 2, 3, 3, 4, 4, 5, 4, 6, 6, 6, 7, 7, 7, 8, 7, 8, 9, 9, 9, 9, 8, 10, 9, 10, 11, 11, 11, 11, 12, 12, 12, 11, 12, 11, 12, 13, 13, 13, 14, 14, 14, 13, 14, 14, 14, 15, 14, 14, 12, 14, 15, 14, 15, 16, 17, 17, 16, 16, 16, 16, 17, 16, 16, 17, 17, 16, 16, 15, 17, 19

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The prime counting function corresponds to A000720.

This sequence has similarities with A294991; a(n) gives approximately the number of intermediate terms to consider in order to compute A316434(n) using the formula of its definition.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Illustration of a(42)

Rémy Sigrist, Density plot of the first 100000000 terms

Rémy Sigrist, C++ program for A321211

EXAMPLE

The first terms, alongside pi(n) and S(n), are:

n a(n) pi(n) S(n)

-- ---- ----- ----------------------

1 1 0 {1}

2 2 1 {1, 2}

3 3 2 {1, 2, 3}