A069518 -id:A069518 - cp's OEIS frontend

A061428 Geometric mean of the digits = 4. In other words, the product of the digits is = 4^k where k is the number of digits.

4, 28, 44, 82, 188, 248, 284, 428, 444, 482, 818, 824, 842, 881, 1488, 1848, 1884, 2288, 2448, 2484, 2828, 2844, 2882, 4188, 4248, 4284, 4428, 4444, 4482, 4818, 4824, 4842, 4881, 8148, 8184, 8228, 8244, 8282, 8418, 8424, 8442, 8481, 8814, 8822, 8841, 12888

Offset: 1

Amarnath Murthy, May 03 2001

			248 is a term as the geometric mean of digits is (2*4*8) = 64 = 4^3.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A061426, A061427, A061429, A061430.

Cf. A028846, A069518.

a061428 n = a061428_list !! (n-1)
a061428_list = g [1] where
   g ds = if product ds == 4 ^ length ds
          then foldr (\d v -> 10 * v + d) 0 ds : g (s ds) else g (s ds)
   s [] = [1]; s (8:ds) = 1 : s ds; s (d:ds) = 2*d : ds
-- Reinhard Zumkeller, Jan 13 2014

from math import prod
from sympy.utilities.iterables import multiset_combinations, multiset_permutations
def auptod(maxdigits):
  n, digs, alst, powsexps2 = 0, 1, [], [(1, 0), (2, 1), (4, 2), (8, 3)]
  for digs in range(1, maxdigits+1):
    target, okdigs = 4**digs, set()
    mcstr = "".join(str(d)*(digs//max(1, r//2)) for d, r in powsexps2)
    for mc in multiset_combinations(mcstr, digs):
      if prod(map(int, mc)) == target:
        n += 1
        okdigs |= set("".join(mp) for mp in multiset_permutations(mc, digs))
    alst += sorted(map(int, okdigs))
  return alst
print(auptod(4)) # Michael S. Branicky, Apr 28 2021

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001

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

Original entry on oeis.org

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

A069516 Geometric mean of digits = 3 and digits are in nondecreasing order.

Original entry on oeis.org

3, 19, 33, 139, 333, 1199, 1339, 3333, 11399, 13339, 33333, 111999, 113399, 133339, 333333, 1113999, 1133399, 1333339, 3333333, 11119999, 11133999, 11333399, 13333339, 33333333, 111139999, 111333999, 113333399, 133333339, 333333333, 1111199999, 1111339999

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.

			1339 belongs to this sequence but 1933 does not.

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

Cf. A061427, A069512, A069518.

a = {}; b = 3; 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, 10^8}]

from math import prod
from sympy.utilities.iterables import multiset_combinations
def aupton(terms):
  n, digits, alst, powsexps3 = 0, 1, [], [(1, 0), (3, 1), (9, 2)]
  while n < terms:
    target = 3**digits
    mcstr = "".join(str(d)*(digits//max(1, r)) for d, r in powsexps3)
    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(31)) # Michael S. Branicky, Apr 28 2021

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

Name edited and a(30) and beyond from Michael S. Branicky, Apr 28 2021

cp's OEIS Frontend

A061428 Geometric mean of the digits = 4. In other words, the product of the digits is = 4^k where k is the number of digits.

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

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A069516 Geometric mean of digits = 3 and digits are in nondecreasing order.

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Mathematica

Python

Extensions