A059092 Zeroless pandigitals expressible as a product of five factors that concatenate to another zeroless pandigital.

129473856, 138729456, 162378594, 164597832, 167495328, 169857324, 172349856, 173429568, 175349286

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

Table of n, a(n) for n=1..9.

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