A096306 - OEIS

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

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OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

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.

CROSSREFS

Sequence in context: A347532 A243911 A289660 * A335187 A231962 A052441

Adjacent sequences: A096303 A096304 A096305 * A096307 A096308 A096309

KEYWORD

base,nonn

AUTHOR

Jason Earls, Jun 26 2004

STATUS

approved