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

1,2

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

Prog

(SageMath) # Function that returns an array of the first n terms.
def A272800(n):
    A, B, k = [0]*n, range(n), 1
    while k<len(B):
        for i in range(floor(len(B)/(k + 1))):
            A[B.pop(k*(i + 1))] = k + 1
        k += 1
    return A
# Danny Rorabaugh, May 13 2016

Crossrefs

Cf. A000960, A100002, A100287.

Sequence in context: A246752 A246650 A264940 * A104513 A357618 A305610

Adjacent sequences: A272797 A272798 A272799 * A272801 A272802 A272803

Keyword

nonn

Author

Max Barrentine, May 06 2016

Status

approved