A096293 Number of iterations of n -> n + (sum of squares of digits of n) needed for the trajectory of n to join the trajectory of A033936.

0, 0, 8, 76, 72, 0, 330, 8, 73, 77, 76, 7, 75, 73, 72, 66, 6, 62, 25, 75, 67, 72, 74, 74, 8, 66, 38, 70, 74, 71, 72, 62, 72, 70, 61, 73, 7, 75, 70, 330, 71, 0, 329, 73, 61, 62, 73, 71, 72, 74, 71, 73, 65, 7, 74, 329, 73, 70, 69, 70, 62, 0, 3, 39, 60, 65, 5, 328, 60, 72, 75, 7, 73

Offset

1,3

Comments

Conjecture: For any positive integer starting value n, iterations of n -> n + (sum of squares of digits of n) will eventually join A033936 (verified for all n up to 20000).

Links

Table of n, a(n) for n=1..73.

Example

a(3)=8 because the trajectory for 1 (sequence A033936) starts
1->2->6->42->62->102->107->157->232->249->350->384->473...
and the trajectory for 3 starts
3->12->17->67->152->182->251->281->350->384->473...
so the sequence beginning with 3 joins A033936 after 8 steps.

Crossrefs

Sequence in context: A111685 A302814 A088376 * A355049 A239549 A247828

Adjacent sequences: A096290 A096291 A096292 * A096294 A096295 A096296

Keyword

base,nonn

Author

Jason Earls, Jun 24 2004

Status

approved