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
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
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