A062237 Positive numbers k which are (sum of digits of k) concatenated with (product of digits of k).

10, 20, 30, 40, 50, 60, 70, 80, 90, 119, 1236, 19135, 19144, 261296, 3634992, 43139968

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

If we exchange sum with product we get 911, 3612, 13519, 14419, 129626, 3499236, 13996843, which are circular permutations of the last seven terms. - Paolo P. Lava, Apr 10 2018

Links

Table of n, a(n) for n=1..16.

Example

1236 has sum of digits 12 and product of digits 36.

Maple

P:=proc(q) local n; for n from 1 to q do
if n=parse(cat(convert(convert(n, base, 10), `+`), convert(convert(n, base, 10), `*`)))
then print(n); fi; od;  end: P(10^8); # Paolo P. Lava, Apr 10 2018

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

Cf. A038364, A038369, A066282.

Sequence in context: A028440 A332046 A166511 * A162467 A033022 A031497

Adjacent sequences: A062234 A062235 A062236 * A062238 A062239 A062240

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