

A272800


Flavius Josephus factor of n.


1



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
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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 nvalues 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


PROG

(Sage) # 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 A305610 A220455
Adjacent sequences: A272797 A272798 A272799 * A272801 A272802 A272803


KEYWORD

nonn


AUTHOR

Max Barrentine, May 06 2016


STATUS

approved



