A069516 -id:A069516 - cp's OEIS frontend

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

Amarnath Murthy, Mar 30 2002

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.

			1128 is a term but 2118 is not.

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

Cf. A061426, A069516, A069518.

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}]

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

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

A069518 Geometric mean of digits = 4 and digits are in nondecreasing order.

Original entry on oeis.org

4, 28, 44, 188, 248, 444, 1488, 2288, 2448, 4444, 12888, 14488, 22488, 24448, 44444, 118888, 124888, 144488, 222888, 224488, 244448, 444444, 1148888, 1228888, 1244888, 1444488, 2224888, 2244488, 2444448, 4444444, 11288888, 11448888, 12248888, 12444888

Offset: 1

Amarnath Murthy, Mar 30 2002

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

			1488 is a term but 1848 is not.

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

Cf. A061428, A069512, A069516.

a = {}; b = 4; 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}]

from math import prod
from sympy.utilities.iterables import multiset_combinations
def auptod(terms):
  n, digits, alst, powsexps2 = 0, 1, [], [(1, 0), (2, 1), (4, 2), (8, 3)]
  while n < terms:
    target = 4**digits
    mcstr = "".join(str(d)*(digits//max(1, r//2)) 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(auptod(34)) # Michael S. Branicky, Apr 28 2021

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

Name edited and a(31) and beyond from Michael S. Branicky, Apr 28 2021

cp's OEIS Frontend

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

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