OFFSET
1,1
COMMENTS
For a d-digit number with d >= 88, the sum and product of the digits together have fewer than d digits. So every element of this sequence has 87 or fewer digits, hence it is finite. - David W. Wilson, Apr 28 2005
EXAMPLE
1236 has sum of digits 12 and product of digits 36.
PROG
(Python)
from math import prod
from sympy.utilities.iterables import multiset_permutations as mp
from itertools import count, islice, combinations_with_replacement as mc
def c(s):
d = list(map(int, s))
return sorted(s) == sorted(str(sum(d)) + str(prod(d)))
def ok(s):
d = list(map(int, s))
return s[0] != '0' and "".join(s) == str(sum(d)) + str(prod(d))
def nd(d): yield from ("".join(m) for m in mc("0123456789", d))
def b(): yield from (s for d in count(1) for s in nd(d) if c(s))
def a(): yield from (int("".join(p)) for s in b() for p in mp(s) if ok(p))
print(list(islice(a(), 16))) # Michael S. Branicky, Jun 30 2022
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Erich Friedman, Jun 30 2001
EXTENSIONS
More terms from Harvey P. Dale, Jul 04 2001
More terms from David W. Wilson, Apr 28 2005; he reports on May 03 2005 that there are no further terms.
Offset corrected by Altug Alkan, Apr 10 2018
STATUS
approved