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A304392 Numbers without a digit 1 with digits in nondecreasing order and the product of digits is a power of 6.

%I A304392 #20 Jun 23 2021 09:59:16
%S A304392 6,23,49,66,229,236,334,389,469,666,2233,2269,2349,2366,2899,3338,
%T A304392 3346,3689,4499,4669,6666,22239,22336,22499,22669,23334,23389,23469,
%U A304392 23666,26899,33368,33449,33466,34899,36689,44699,46669,66666,88999,222299,222333,222369,223349
%N A304392 Numbers without a digit 1 with digits in nondecreasing order and the product of digits is a power of 6.
%C A304392 Applying any of the following to terms in this sequence in any order gives a term from A276038: - Prepend a 1. - Permute digits. - Do nothing.
%C A304392 Subsequence of A276038.
%H A304392 Michael S. Branicky, <a href="/A304392/b304392.txt">Table of n, a(n) for n = 1..10656</a> (all terms with <= 23 digits)
%e A304392 229 is in the sequence because it has digits in nondecreasing order, no digit 1 and a product of digits 2*2*9 = 36 which is a power of 6.
%t A304392 Select[Range[10^6], And[FreeQ[#, 1], AllTrue[Differences@ #, # > -1 &], IntegerQ@ Log[6, Times @@ #]] &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Jun 30 2018 *)
%o A304392 (PARI) is(n) = my(d = digits(n), p = prod(i = 1, #d, d[i])); d[1] >= 2 && vecsort(d) == d && 6^logint(p, 6) == p
%o A304392 (Python)
%o A304392 from math import prod
%o A304392 from sympy.utilities.iterables import multiset_combinations
%o A304392 def auptod(maxdigs):
%o A304392   n, digs, alst, targets = 0, 1, [], set(6**i for i in range(1, maxdigs*3))
%o A304392   for digs in range(1, maxdigs+1):
%o A304392     mcstr = "".join(str(d)*digs for d in "234689")
%o A304392     for mc in multiset_combinations(mcstr, digs):
%o A304392       if prod(map(int, mc)) in targets: alst.append(int("".join(mc)))
%o A304392   return alst
%o A304392 print(auptod(6)) # _Michael S. Branicky_, Jun 23 2021
%Y A304392 Cf. A009994, A276038.
%K A304392 nonn,base
%O A304392 1,1
%A A304392 _David A. Corneth_, Jun 20 2018