A070561 -id:A070561 - cp's OEIS frontend

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

N. J. A. Sloane, May 07 2002

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.

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

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

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

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

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 *)

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, ", "))

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

A070560 a(0) = 1; for n > 0, a(n) = (fecundity of n) + 2.

Original entry on oeis.org

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, 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, 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

Offset: 0

N. J. A. Sloane, May 07 2002

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

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

Cf. A070561, A070562, A031346, A003001.

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

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

cp's OEIS Frontend

A070562 Fecundity of n.

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