A096306 Number of iterations of n -> n + (largest digit of n) needed for the trajectory of n to join the trajectory of A045844.

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, 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, 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

Offset: 1

Author

Jason Earls, Jun 26 2004

Keywords

• base
• nonn

Comments

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

Examples

			a(25)=3 because the trajectory for 1 (sequence A045844) starts
1->2->4->8->16->22->24->28->36->42->46...
and the trajectory for 25 starts
25->30->33->36->42->46->52->57...
so the sequence beginning with 25 joins A045844 after 3 steps.