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URL: https://oeis.org/A069512

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A069512
Geometric mean of digits = 2 and digits are in nondecreasing order.
4
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
1,1
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.
LINKS
EXAMPLE
1128 is a term but 2118 is not.
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}]
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Mar 30 2002
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
STATUS
approved