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Number of iterations of n -> n + (largest digit of n) needed for the trajectory of n to join the trajectory of A045844.
0

%I #3 Dec 15 2017 17:36:43

%S 0,0,18,0,19,17,16,0,15,18,17,16,1,15,2,0,1,14,1,1,15,0,14,0,3,13,3,0,

%T 2,2,3,12,1,2,11,0,10,1,9,10,69,0,9,9,68,0,8,8,66,67,8,0,66,7,66,7,0,

%U 65,6,65,62,6,63,0,63,64,61,5,62,0,62,63,63,60,4,4,0,61,62,62,59,3,3,0,2,60

%N Number of iterations of n -> n + (largest digit of n) needed for the trajectory of n to join the trajectory of A045844.

%C Conjecture: For any positive integer starting value n, iterations of n -> n + (largest digit of n) will eventually join A045844.

%e a(25)=3 because the trajectory for 1 (sequence A045844) starts

%e 1->2->4->8->16->22->24->28->36->42->46...

%e and the trajectory for 25 starts

%e 25->30->33->36->42->46->52->57...

%e so the sequence beginning with 25 joins A045844 after 3 steps.

%K base,nonn

%O 1,3

%A _Jason Earls_, Jun 26 2004