A272800 Flavius Josephus factor of n.

0, 2, 0, 2, 3, 2, 0, 2, 4, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 4, 2, 3, 2, 6, 2, 0, 2, 3, 2, 7, 2, 4, 2, 3, 2, 5, 2, 0, 2, 3, 2, 8, 2, 4, 2, 3, 2, 0, 2, 6, 2, 3, 2, 5, 2, 4, 2, 3, 2, 9, 2, 0, 2, 3, 2, 10, 2, 4, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 4, 2, 3, 2, 6, 2

Offset: 1

Author

Max Barrentine, May 06 2016

Keywords

• nonn

Comments

This sequence is analogous to the smallest prime factor of n. If n is a member of A000960, a(n) = 0, otherwise a(n) = the (k+1)-st step that rejects n from Flavius Josephus' sieve.

The n-values of records of this sequence are given by A100287 (see 2004 comment by Sloane).

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A000960, A100002, A100287.

Programs

Sage

# Function that returns an array of the first n terms.
def A272800(n):
    A, B, k = [0]*n, range(n), 1
    while kDanny Rorabaugh, May 13 2016