OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Robert Bilinski, Sep 21 2020
EXTENSIONS
More terms from Amiram Eldar, Sep 22 2020
Offset changed by Robert Israel, Apr 12 2021
STATUS
approved