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 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 (list; graph; refs; listen; history; text; internal format)
 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' 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

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Last modified December 7 15:42 EST 2023. Contains 367658 sequences. (Running on oeis4.)