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.

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, 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, 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

Offset: 1

Author

Jason Earls, Jun 23 2004

Keywords

• base
• nonn

Comments

Loomis has verified that all n up to 1000000 eventually join the trajectory of A063108.

Examples

			a(3)=5 because the trajectory for 1 (Sequence A063108) starts
1->2->4->8->16->22->26->38->62->74...
and the sequence for 3 starts
3->6->12->14->18->26->38->62->74...
so the sequence beginning with 3 joins A063108 after 5 steps.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• P. A. Loomis, An Interesting Family of Iterated Sequences.
• P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151.
• P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy]
• Paul Tek, C program for this sequence
• Index entries for Colombian or self numbers and related sequences

Programs

C

See Link section.