

A062237


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


4



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

1,1


COMMENTS

For a ddigit 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



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))


CROSSREFS



KEYWORD

nonn,base,fini,full


AUTHOR



EXTENSIONS

More terms from David W. Wilson, Apr 28 2005; he reports on May 03 2005 that there are no further terms.


STATUS

approved



