A070561 a(0) = 0; for n > 0, a(n) = (fecundity of n) + 1.

0, 11, 10, 10, 9, 2, 9, 8, 8, 7, 1, 9, 8, 8, 7, 2, 7, 7, 6, 4, 1, 6, 6, 5, 6, 3, 5, 6, 3, 4, 1, 4, 5, 3, 3, 2, 4, 4, 4, 3, 1, 5, 2, 3, 2, 4, 2, 3, 2, 5, 1, 6, 4, 9, 3, 2, 5, 3, 3, 2, 1, 3, 3, 6, 6, 3, 2, 2, 8, 6, 1, 5, 5, 3, 2, 2, 7, 6, 4, 3, 1, 5, 3, 2, 8, 4, 4, 4, 5, 4, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1

Offset

0,2

Comments

Start with n, repeatedly replace x by x + product of digits of x until the product of digits reaches 0; fecundity = number of steps - 1.

Equivalently, with A230099 = f, a(n) is the number k of distinct values that are obtained with iterations: n, f(n), f(f(n)), f(f(f(n))), ... until a term of this sequence contains a 0. - Bernard Schott, Jul 31 2023

Links

Table of n, a(n) for n=0..103.

Diophante, A306, Les nombres féconds (in French).

Formula

a(n) = 1 iff n positive is in A011540. - Bernard Schott, Jul 31 2023

Example

1 -> 2 -> 4 -> 8 -> 16 -> 22 -> 26 -> 38 -> 62 -> 74 ->102 -> 102 -> ... has fecundity 10.

Mathematica

f[n_] := Length@FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 1; f[0] = 0; Array[f, 105, 0] (* Robert G. Wilson v, Jun 27 2010 *)

Crossrefs

Cf. A011540, A070560, A070562, A031346, A003001, A230099.

Sequence in context: A291467 A112952 A343959 * A059941 A086100 A182782

Adjacent sequences: A070558 A070559 A070560 * A070562 A070563 A070564

Keyword

nonn,easy,base

Author

N. J. A. Sloane, May 07 2002

Extensions

More terms from Robert G. Wilson v, Jun 27 2010

Status

approved