A070560 - OEIS

%I #7 Jul 19 2015 01:09:08

%S 1,12,11,11,10,3,10,9,9,8,2,10,9,9,8,3,8,8,7,5,2,7,7,6,7,4,6,7,4,5,2,

%T 5,6,4,4,3,5,5,5,4,2,6,3,4,3,5,3,4,3,6,2,7,5,10,4,3,6,4,4,3,2,4,4,7,7,

%U 4,3,3,9,7,2,6,6,4,3,3,8,7,5,4,2,6,4,3,9,5,5,5,6,5,2,3,3,3,3,3,3,3,3,3,2,2

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

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

%e 1 -> 2 -> 4 -> 8 -> 16 -> 22 -> 26 -> 38 -> 62 -> 74 -> 102 -> 0 has fecundity 10.

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

%Y Cf. A070561, A070562, A031346, A003001.

%K nonn,easy,base

%O 0,2

%A _N. J. A. Sloane_, May 07 2002

%E More terms from _Robert G. Wilson v_, Jun 27 2010