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%I #28 Feb 19 2024 10:32:03
%S 10,20,30,40,50,60,70,80,90,119,1236,19135,19144,261296,3634992,
%T 43139968
%N Positive numbers k which are (sum of digits of k) concatenated with (product of digits of k).
%C 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
%e 1236 has sum of digits 12 and product of digits 36.
%o (Python)
%o from math import prod
%o from sympy.utilities.iterables import multiset_permutations as mp
%o from itertools import count, islice, combinations_with_replacement as mc
%o def c(s):
%o d = list(map(int, s))
%o return sorted(s) == sorted(str(sum(d)) + str(prod(d)))
%o def ok(s):
%o d = list(map(int, s))
%o return s[0] != '0' and "".join(s) == str(sum(d)) + str(prod(d))
%o def nd(d): yield from ("".join(m) for m in mc("0123456789", d))
%o def b(): yield from (s for d in count(1) for s in nd(d) if c(s))
%o def a(): yield from (int("".join(p)) for s in b() for p in mp(s) if ok(p))
%o print(list(islice(a(), 16))) # _Michael S. Branicky_, Jun 30 2022
%Y Cf. A038364, A038369, A066282.
%K nonn,base,fini,full
%O 1,1
%A _Erich Friedman_, Jun 30 2001
%E More terms from _Harvey P. Dale_, Jul 04 2001
%E More terms from _David W. Wilson_, Apr 28 2005; he reports on May 03 2005 that there are no further terms.
%E Offset corrected by _Altug Alkan_, Apr 10 2018
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