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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.)