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

6, 23, 49, 66, 229, 236, 334, 389, 469, 666, 2233, 2269, 2349, 2366, 2899, 3338, 3346, 3689, 4499, 4669, 6666, 22239, 22336, 22499, 22669, 23334, 23389, 23469, 23666, 26899, 33368, 33449, 33466, 34899, 36689, 44699, 46669, 66666, 88999, 222299, 222333, 222369, 223349

Offset: 1

Author

David A. Corneth, Jun 20 2018

Keywords

• nonn
• base

Comments

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.

Subsequence of A276038.

Examples

			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.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10656 (all terms with <= 23 digits)

Crossrefs

Cf. A009994, A276038.

Programs

Mathematica

Select[Range[10^6], And[FreeQ[#, 1], AllTrue[Differences@ #, # > -1 &], IntegerQ@ Log[6, Times @@ #]] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jun 30 2018 *)

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

Python

from math import prod
from sympy.utilities.iterables import multiset_combinations
def auptod(maxdigs):
  n, digs, alst, targets = 0, 1, [], set(6**i for i in range(1, maxdigs*3))
  for digs in range(1, maxdigs+1):
    mcstr = "".join(str(d)*digs for d in "234689")
    for mc in multiset_combinations(mcstr, digs):
      if prod(map(int, mc)) in targets: alst.append(int("".join(mc)))
  return alst
print(auptod(6)) # Michael S. Branicky, Jun 23 2021