login
A070561
a(0) = 0; for n > 0, a(n) = (fecundity of n) + 1.
2
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
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