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 A096287 Number of iterations of n -> n + (product of nonzero digits of n) needed for the trajectory of n to join the trajectory of A063108. 3

%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 (2003-2004), 147-151.

%H P. A. Loomis, <a href="/A063108/a063108.pdf">An Introduction to Digit Product Sequences</a>, J. Rec. Math., 32 (2003-2004), 147-151. [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.