A070562 Fecundity of n.

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

Offset

0,2

Comments

Start with x=n, repeatedly replace x by x + product of digits of x until the product is 0; fecundity = number of steps. a(0) = 0 by convention.

References

P. Tougne, Jeux Mathematiques column, Pour La Science (French edition of "Scientific American"), Vol. 82, Aug. 1984, Prob. 6, pp. 101, 104.

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Example

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

Mathematica

f[ n_ ] := Block[ {a=n, b, c=0}, While[ b=Times@@IntegerDigits[ a ]; b>0, a=a+b; c++ ]; c ]; f[ 0 ]=0; Table[ f[ n ], {n, 0, 100} ]
f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f, 105, 0] (* Robert G. Wilson v, Jun 27 2010 *)

Prog

(PARI) prodig(n) = local(s, d); if(n==0, s=0, s=1; while(n>0, d=divrem(n, 10); n=d[1 ]; s=s*d[2 ])); s for(n=0, 92, x=n; c=0; while((d=prodig(x))!=0, c++; x=x+d); print1(c, ", "))

Crossrefs

Cf. A070560. A070561, A031346, A003001, A070061, A070257.

Sequence in context: A132674 A090293 A164732 * A216557 A070641 A231471

Adjacent sequences: A070559 A070560 A070561 * A070563 A070564 A070565

Keyword

nonn,easy,base

Author

N. J. A. Sloane, May 07 2002

Extensions

Edited and extended by Klaus Brockhaus, May 08 2002

Clarified the definition of fecundity and improved the Mathematica program. - T. D. Noe, Oct 06 2008

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

Status

approved