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Product of digits of n in factorial base.
12

%I #27 Mar 22 2021 03:41:57

%S 0,1,0,1,0,2,0,0,0,1,0,2,0,0,0,2,0,4,0,0,0,3,0,6,0,0,0,0,0,0,0,0,0,1,

%T 0,2,0,0,0,2,0,4,0,0,0,3,0,6,0,0,0,0,0,0,0,0,0,2,0,4,0,0,0,4,0,8,0,0,

%U 0,6,0,12,0,0,0,0,0,0,0,0,0,3,0,6,0,0,0,6,0,12,0,0,0,9,0,18

%N Product of digits of n in factorial base.

%H Antti Karttunen, <a href="/A208575/b208575.txt">Table of n, a(n) for n = 0..10080</a>

%H M. R. Diamond and D. D. Reidpath, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/persistence/PERSIST.PDF">A counterexample to conjectures by Sloane and Erdos concerning the persistence of numbers</a>, Journal of Recreational Mathematics 29:2 (1998), pp. 89-92.

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

%t (* For the definition of the factorial base version of IntegerDigits, see A007623 *) Table[Times@@factBaseIntDs[n], {n, 0, 99}] (* _Alonso del Arte_, Feb 28 2012 *)

%o (PARI) a(n)=my(k=1,s=1);while(n,s*=n%k++;n\=k);s

%o (Python)

%o from operator import mul

%o def A(n, p=2):

%o return n if n<p else A(n//p, p+1)*10 + n%p

%o def a(n):

%o x=str(A(n - 1))

%o return 0 if "0" in x else reduce(mul, [int(i) for i in x])

%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jun 19 2017

%Y Cf. A007623, A007954, A031346, A208576, A208277, A227153, A227154, A286590.

%K nonn,base

%O 0,6

%A _Charles R Greathouse IV_, Feb 28 2012