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A059092
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Zeroless pandigitals expressible as a product of five factors that concatenate to another zeroless pandigital.
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0
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OFFSET
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1,1
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COMMENTS
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Here, pandigital means each nonzero digit appears exactly once.
There are no other terms (via exhaustive search; see Python program). (End)
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REFERENCES
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J. S. Madachy, Madachy's Mathematical Recreations, pp. 161, Dover NY 1979
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LINKS
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EXAMPLE
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We have, for instance, the five-factor pandigital decomposition for 172349856 = 6*7*84*92*531.
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
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PROG
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(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)
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CROSSREFS
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KEYWORD
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fini,full,base,nonn
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AUTHOR
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STATUS
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approved
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