A156055 Define a map f by f(0) = f(1) = 0, otherwise f(k) = A087712(k); then a(n) is the number of steps for the trajectory of n under repeated iteration of f to "terminate".

1, 2, 3, 6, 4, 30, 7, 54, 3, 32, 5, 29, 31, 0, 3, 19, 8, 112, 55, 15, 27, 3, 3, 26, 1, 20, 223, 102, 33, 13, 6, 162, 1, 9, 10, 75, 30, 113, 21

Offset: 1

Author

Robert G. Wilson v, Feb 02 2009

Keywords

• base
• nonn
• more

Comments

Here "terminate" means reaching 0 or a cycle.

From M. F. Hasler, Feb 11 2009: (Start)

"Reaching a cycle" could be better defined: does it mean "reach a value that occurred earlier" or "reach an element belonging to a cycle"?

I think the second is the case, but the value 0 is currently listed at n=14, wouldn't it correspond to x=15 = least element of a nontrivial cycle?

So would the offset be 2 ? or is there a missing term (since the first terms 1,2,3 seem well to correspond to x=1,2,3)? (End)

Examples

			a(4) = 6 because 4 -> [{2,2}->{1,1}] ->[{11}->{5}] -> [{5}->{3}] -> [{3}->{2}] -> [{2}->{1}] -> [{1}->{0}].
		

Crossrefs

A variant of A098282, which is the official version of this sequence.

Cf. A087712.

Programs

Mathematica

f[n_] := FromDigits@ Flatten[ IntegerDigits@# & /@ (PrimePi@# & /@ Flatten[ Table[ First@#, {Last@#}] & /@ FactorInteger@n])]; g[n_] := Length@ NestWhileList[f, n, UnsameQ, All] - 2; Array[g, 39]

Extensions

Edited by N. J. A. Sloane, Feb 10 2009