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A101183 Number of times (>0) function f must be applied in A100800 to arrive at multiple of n, or 0 if multiple of n is never reached.

%I A101183 #8 May 14 2019 14:51:23
%S A101183 1,1,1,1,1,1,1,1,1,14,32,3,12,36,3,31,10,2,71,8,8,8,11,8,67,8,3,35,35,
%T A101183 10,31,53,22,45,38,4,59,70,44,27,27,19,44,36,5,14,47,42,33,66,16,33,
%U A101183 42,11,105,151,5,92,69,7,7,48,6,23,20,22,7,62,22,145,7,7,20,7,58,7,184,44
%N A101183 Number of times (>0) function f must be applied in A100800 to arrive at multiple of n, or 0 if multiple of n is never reached.
%C A101183 Conjecture: No term is zero.
%H A101183 Robert Israel, <a href="/A101183/b101183.txt">Table of n, a(n) for n = 1..10000</a>
%e A101183 a(10) = 14 since f has to be applied 14 times to 10 to arrive at 130, a multiple of 10.
%p A101183 f:= n -> n + convert(convert(n,base,10),`+`):
%p A101183 g:= proc(n) local j,t;
%p A101183   t:= n;
%p A101183   for j from 1 do
%p A101183     t:= f(t);
%p A101183     if t mod n = 0 then return j fi
%p A101183   od
%p A101183 end proc:
%p A101183 map(g, [$1..100]); # _Robert Israel_, May 14 2019
%Y A101183 Cf. A100800, A100801.
%K A101183 base,look,nonn
%O A101183 1,10
%A A101183 _Ray Chandler_, Dec 19 2004