A069516 Geometric mean of digits = 3 and digits are in nondecreasing order.

3, 19, 33, 139, 333, 1199, 1339, 3333, 11399, 13339, 33333, 111999, 113399, 133339, 333333, 1113999, 1133399, 1333339, 3333333, 11119999, 11133999, 11333399, 13333339, 33333333, 111139999, 111333999, 113333399, 133333339, 333333333, 1111199999, 1111339999

Offset: 1

Author

Amarnath Murthy, Mar 30 2002

Keywords

• nonn
• base

Comments

No number is obtainable by permuting the digits of other members - only one with ascending order of digits is included.

Examples

			1339 belongs to this sequence but 1933 does not.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061427, A069512, A069518.

Programs

Mathematica

a = {}; b = 3; Do[c = Apply[ Times, IntegerDigits[n]]/b^Floor[ Log[10, n] + 1]; If[c == 1 && Position[a, FromDigits[ Sort[ IntegerDigits[n]]]] == {}, Print[n]; a = Append[a, n]], {n, 1, 10^8}]

Python

from math import prod
from sympy.utilities.iterables import multiset_combinations
def aupton(terms):
  n, digits, alst, powsexps3 = 0, 1, [], [(1, 0), (3, 1), (9, 2)]
  while n < terms:
    target = 3**digits
    mcstr = "".join(str(d)*(digits//max(1, r)) for d, r in powsexps3)
    for mc in multiset_combinations(mcstr, digits):
      if prod(map(int, mc)) == target:
        n += 1
        alst.append(int("".join(mc)))
        if n == terms: break
    else: digits += 1
  return alst
print(aupton(31)) # Michael S. Branicky, Apr 28 2021

Extensions

Edited and extended by Robert G. Wilson v, Apr 01 2002

Name edited and a(30) and beyond from Michael S. Branicky, Apr 28 2021