%I
%S 0,0,5,0,6,4,3,0,2,5,4,3,1,2,2,0,3,1,5,1,10,0,9,2,7,0,9,4,8,8,5,1,7,4,
%T 6,2,15,0,2,4,8,6,5,3,7,3,7,4,16,5,17,1,2,1,4,16,7,14,1,2,4,0,322,3,6,
%U 1,3,1,17,2,16,16,17,0,6,2,1,15,14,3,321,14,4,1,15,15,13,2,320,12,3,6,2,16
%N Number of iterations of n > n + (product of nonzero digits of n) needed for the trajectory of n to join the trajectory of A063108.
%C Loomis has verified that all n up to 1000000 eventually join the trajectory of A063108.
%H Paul Tek, <a href="/A096287/b096287.txt">Table of n, a(n) for n = 1..10000</a>
%H P. A. Loomis, <a href="http://facstaff.bloomu.edu/ploomis/sequences.html">An Interesting Family of Iterated Sequences</a>.
%H P. A. Loomis, <a href="http://facstaff.bloomu.edu/ploomis/itseq4.ps">An Introduction to Digit Product Sequences</a>, J. Rec. Math., 32 (20032004), 147151.
%H P. A. Loomis, <a href="/A063108/a063108.pdf">An Introduction to Digit Product Sequences</a>, J. Rec. Math., 32 (20032004), 147151. [Annotated archived copy]
%H Paul Tek, <a href="/A096287/a096287.txt">C program for this sequence</a>
%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e a(3)=5 because the trajectory for 1 (Sequence A063108) starts
%e 1>2>4>8>16>22>26>38>62>74...
%e and the sequence for 3 starts
%e 3>6>12>14>18>26>38>62>74...
%e so the sequence beginning with 3 joins A063108 after 5 steps.
%o (C) See Link section.
%K base,nonn
%O 1,3
%A Jason Earls (zevi_35711(AT)yahoo.com), Jun 23 2004
