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

1,3

Comments

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

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

Example

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.

Prog

(C) See Link section.

Crossrefs

Sequence in context: A159751 A190914 A153458 * A240243 A330864 A144483

Adjacent sequences: A096284 A096285 A096286 * A096288 A096289 A096290

Keyword

base,nonn

Author

Jason Earls, Jun 23 2004

Status

approved