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 A059092 Zeroless pandigitals expressible as a product of five factors that concatenate to another zeroless pandigital. 0
 129473856, 138729456, 162378594, 164597832, 167495328, 169857324, 172349856, 173429568, 175349286 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Michael S. Branicky, Aug 05 2022: (Start) Here, pandigital means each nonzero digit appears exactly once. There are no other terms (via exhaustive search; see Python program). (End) REFERENCES J. S. Madachy, Madachy's Mathematical Recreations, pp. 161, Dover NY 1979 LINKS EXAMPLE We have, for instance, the five-factor pandigital decomposition for 172349856 = 6*7*84*92*531. From Lekraj Beedassy, Dec 18 2007: (Start) a(1) = 129473856 = 4*6*8*93*7251, a(2) = 138729456 = 6*8*9*71*4523, a(3) = 162378594 = 6*7*9*51*8423, a(4) = 164597832 = 6*7*9*524*831, a(5) = 167495328 = 6*7*52*84*913, a(6) = 169857324 = 6*7*54*91*823, a(7) = 172349856 = 6*7*84*92*531, a(8) = 173429568 = 6*8*53*92*741, a(9) = 175349286 = 7*9*54*83*621. (End) 123879456 = 9*9*712*6*358 is not a term since 9 appears twice on the right. - Michael S. Branicky, Aug 05 2022 PROG (Python) from itertools import permutations def zpan(n): s = str(n); return "0" not in s and len(s) == len(set(s)) == 9 def afind(verbose=False): aset = set() for p in permutations("987654321"): for mlocs in ["1234", "1235", "1236", "1246", "1357"]: ops = ["*" if str(i) in mlocs else "" for i in range(9)] e = "".join(ops[i]+p[i] for i in range(9)) t = eval(e) if zpan(t) and t not in aset: aset.add(t) if verbose: print(f"{t} = {e}") return sorted(aset) print(afind(verbose=True)) # Michael S. Branicky, Aug 05 2022 CROSSREFS Sequence in context: A036341 A184648 A258262 * A147715 A251400 A251281 Adjacent sequences: A059089 A059090 A059091 * A059093 A059094 A059095 KEYWORD fini,full,base,nonn AUTHOR Lekraj Beedassy, Jun 13 2002 STATUS approved

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Last modified November 29 12:29 EST 2022. Contains 358427 sequences. (Running on oeis4.)