A096303 Number of iterations of n -> n + (number of 1's in binary representation of n) needed for the trajectory of n to join the trajectory of A010062.

0, 0, 0, 1, 0, 4, 0, 3, 2, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 6, 0, 2, 5, 0, 4, 1, 0, 3, 2, 0, 3, 2, 1, 1, 0, 5, 0, 2, 4, 0, 3, 1, 0, 2, 7, 0, 7, 1, 6, 1, 0, 5, 3, 0, 2, 4, 2, 1, 0, 3, 1, 6, 0, 0, 2, 0, 1, 5, 0, 2, 4, 0, 3, 1, 0, 2, 5, 0, 5, 1, 4, 1, 0, 3, 10, 0, 2, 2, 9, 1, 0, 1, 8, 1, 0, 8, 0, 7, 7, 0, 6, 6, 6, 0

Offset: 1

Author

Jason Earls, Jun 25 2004

Keywords

• base
• nonn

Comments

Conjecture: For any positive integer starting value n, iterations of n -> n + (number of 1's in binary representation of n) will eventually join A010062.

Examples

			a(6)=4 because the trajectory for 1 (sequence A010062) starts
1->2->3->5->7->10->12->14->17->19->22->25...
and the trajectory for 6 starts
6->8->9->11->14->17->19->22->25->28->31->36...
so the sequence beginning with 6 joins A010062 after 4 steps.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A010062.

For records see A229743, A229744.

Programs

PARI

a(n) = { my (o=1); for (k=0, oo, while (oRémy Sigrist, Apr 05 2020