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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A009994, A276038.

Sequence in context: A081097 A031293 A250647 * A235332 A026817 A022269

Adjacent sequences: A304389 A304390 A304391 * A304393 A304394 A304395

Keyword

nonn,base

Author

David A. Corneth, Jun 20 2018

Status

approved