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

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

Author

Robert Bilinski, Sep 21 2020

Keywords

• nonn
• easy
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A070562, A070061, A070257.

Programs

Maple

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

Mathematica

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

Python

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

Extensions

More terms from Amiram Eldar, Sep 22 2020

Offset changed by Robert Israel, Apr 12 2021