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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 (list; graph; refs; listen; history; text; internal format)
 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 Michael S. Branicky, Table of n, a(n) for n = 1..10000 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 Cf. A061426, A069516, A069518. Sequence in context: A061426 A190045 A247035 * A328217 A116639 A220274 Adjacent sequences:  A069509 A069510 A069511 * A069513 A069514 A069515 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

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Last modified August 5 06:37 EDT 2021. Contains 346458 sequences. (Running on oeis4.)