A069512 Geometric mean of digits = 2 and digits are in nondecreasing order.

2, 14, 22, 118, 124, 222, 1128, 1144, 1224, 2222, 11148, 11228, 11244, 12224, 22222, 111188, 111248, 111444, 112228, 112244, 122224, 222222, 1111288, 1111448, 1112248, 1112444, 1122228, 1122244, 1222224, 2222222, 11111488, 11112288, 11112448, 11114444

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. Product of the digits = 2^k where k is the number of digits.

Examples

			1128 is a term but 2118 is not.
		

Links

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

Crossrefs

Cf. A061426, A069516, A069518.

Programs

Mathematica

a = {}; b = 2; 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, 10^7}]

Python

from math import prod
from sympy.utilities.iterables import multiset_combinations
def aupton(terms):
  n, digits, alst, powsexps2 = 0, 1, [], [(1,0), (2,1), (4,2), (8,3)]
  while n < terms:
    target = 2**digits
    mcstr = "".join(str(d)*(digits//max(1, r)) for d, r in powsexps2)
    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(34)) # Michael S. Branicky, Feb 14 2021

Extensions

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

a(31) corrected by and a(33) and beyond from Michael S. Branicky, Feb 14 2021