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Flavius Josephus factor of n.
1

%I #16 Jun 24 2020 16:57:09

%S 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,

%T 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,

%U 4,2,3,2,7,2,5,2,3,2,0,2,4,2,3,2,6,2

%N Flavius Josephus factor of n.

%C 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.

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

%H Danny Rorabaugh, <a href="/A272800/b272800.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>

%o (Sage) # Function that returns an array of the first n terms.

%o def A272800(n):

%o A, B, k = [0]*n, range(n), 1

%o while k<len(B):

%o for i in range(floor(len(B)/(k + 1))):

%o A[B.pop(k*(i + 1))] = k + 1

%o k += 1

%o return A

%o # _Danny Rorabaugh_, May 13 2016

%Y Cf. A000960, A100002, A100287.

%K nonn

%O 1,2

%A _Max Barrentine_, May 06 2016