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%I #15 Aug 05 2022 07:41:01
%S 129473856,138729456,162378594,164597832,167495328,169857324,
%T 172349856,173429568,175349286
%N Zeroless pandigitals expressible as a product of five factors that concatenate to another zeroless pandigital.
%C From _Michael S. Branicky_, Aug 05 2022: (Start)
%C Here, pandigital means each nonzero digit appears exactly once.
%C There are no other terms (via exhaustive search; see Python program). (End)
%D J. S. Madachy, Madachy's Mathematical Recreations, pp. 161, Dover NY 1979
%e We have, for instance, the five-factor pandigital decomposition for 172349856 = 6*7*84*92*531.
%e From _Lekraj Beedassy_, Dec 18 2007: (Start)
%e a(1) = 129473856 = 4*6*8*93*7251,
%e a(2) = 138729456 = 6*8*9*71*4523,
%e a(3) = 162378594 = 6*7*9*51*8423,
%e a(4) = 164597832 = 6*7*9*524*831,
%e a(5) = 167495328 = 6*7*52*84*913,
%e a(6) = 169857324 = 6*7*54*91*823,
%e a(7) = 172349856 = 6*7*84*92*531,
%e a(8) = 173429568 = 6*8*53*92*741,
%e a(9) = 175349286 = 7*9*54*83*621. (End)
%e 123879456 = 9*9*712*6*358 is not a term since 9 appears twice on the right. - _Michael S. Branicky_, Aug 05 2022
%o (Python)
%o from itertools import permutations
%o def zpan(n): s = str(n); return "0" not in s and len(s) == len(set(s)) == 9
%o def afind(verbose=False):
%o aset = set()
%o for p in permutations("987654321"):
%o for mlocs in ["1234", "1235", "1236", "1246", "1357"]:
%o ops = ["*" if str(i) in mlocs else "" for i in range(9)]
%o e = "".join(ops[i]+p[i] for i in range(9))
%o t = eval(e)
%o if zpan(t) and t not in aset:
%o aset.add(t)
%o if verbose: print(f"{t} = {e}")
%o return sorted(aset)
%o print(afind(verbose=True)) # _Michael S. Branicky_, Aug 05 2022
%K fini,full,base,nonn
%O 1,1
%A _Lekraj Beedassy_, Jun 13 2002
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