A070061 -id:A070061 - 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

A070257 Fecundity of n sets a new record.

Original entry on oeis.org

1, 187, 3237326, 3515987, 22572473, 516675965, 516963965, 41863638649, 35632297938395

Offset: 1

Jason Earls, May 09 2002

a(9) > 10^11. - Donovan Johnson, Jun 23 2011

a(10) > 2.75*10^14. - Giovanni Resta, Jun 04 2013

Cf. A070562, A070061.

a(5)-a(7) from Donovan Johnson, Jul 29 2009
a(8) from Donovan Johnson, Jun 23 2011
a(9) from Giovanni Resta, Jun 04 2013

A337789 Numbers k such that trajectory of k under repeated calculation of fecundity (x -> A070562(x)) eventually reaches 0.

Original entry on oeis.org

0, 1, 5, 10, 15, 18, 20, 21, 22, 24, 27, 30, 35, 40, 42, 44, 46, 48, 50, 51, 55, 59, 60, 63, 64, 66, 67, 69, 70, 74, 75, 77, 80, 83, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 115, 118, 120, 121, 122, 124, 127

Offset: 1

Robert Bilinski, Sep 21 2020

			5 is a term in the sequence because the fecundity of 5 is 1, the fecundity of 1 is 10 and the fecundity of 10 is 0.
7 is not a term in the sequence because the fecundity of 7 is 7 and therefore the fecundity will never become 0.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A070562, A070061, A070257.

fec:= proc(n) local k, x,t;
  x:= n;
  for k from 0 do
    t:= convert(convert(x,base,10),`*`);
    if t = 0 then return k fi;
    x:= x+t
  od
end proc:
filter:= proc(n) local v; option remember;
    v:= fec(n);
    if v = 0 then true
    elif v = n then false
    else procname(v)
    fi
end proc:
select(filter, [$0..1000]); # Robert Israel, Apr 12 2021

fec[n_] := Length @ FixedPointList[# + Times @@ IntegerDigits[#] &, n] - 2; Select[Range[0, 100], FixedPoint[fec, #] == 0 &] (* Amiram Eldar, Sep 22 2020 *)

from math import prod
from functools import lru_cache
def pd(n): return prod(map(int, str(n)))
def A070562(n):
  s = 0
  while pd(n) != 0: n, s = n + pd(n), s + 1
  return s
@lru_cache(maxsize=None)
def ok(n):
  fn = A070562(n)
  if fn == 0: return True
  if fn == n: return False
  return ok(fn)
print(list(filter(ok, range(128)))) # Michael S. Branicky, Apr 12 2021

More terms from Amiram Eldar, Sep 22 2020

Offset changed by Robert Israel, Apr 12 2021

cp's OEIS Frontend

A070562 Fecundity of n.

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A070257 Fecundity of n sets a new record.

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A337789 Numbers k such that trajectory of k under repeated calculation of fecundity (x -> A070562(x)) eventually reaches 0.

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Mathematica

Python

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