A061430 -id:A061430 - cp's OEIS frontend

A285094 Corresponding values of geometric means of digits of numbers from A061430.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 0, 2, 4, 0, 3, 0, 2, 4, 6, 0, 5, 0, 6, 0, 7, 0, 4, 8, 0, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 3, 0, 2, 0, 0, 0, 0, 2, 4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 4, 0

Offset: 0

Jaroslav Krizek, Apr 14 2017

Jaroslav Krizek, Table of n, a(n) for n = 0..3000

Cf. A061430 (numbers with integer geometric mean of digits in base 10).

Sequences of numbers n such that a(n) = k for k = 0 - 9: A011540 (k = 0), A002275 (k = 1), A061426 (k = 2), A061427 (k = 3), A061428 (k = 4), A002279 (k = 5), A061429 (k = 6), A002281 (k = 7), A002282 (k = 8), A002283 (k = 9).

[0] cat [Floor(&*Intseq(n) ^ (1/#Intseq(n))): n in [1..100000] | IsIntegral(&*Intseq(n) ^ (1/#Intseq(n)))];

A061426 Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digits.

Original entry on oeis.org

2, 14, 22, 41, 118, 124, 142, 181, 214, 222, 241, 412, 421, 811, 1128, 1144, 1182, 1218, 1224, 1242, 1281, 1414, 1422, 1441, 1812, 1821, 2118, 2124, 2142, 2181, 2214, 2222, 2241, 2412, 2421, 2811, 4114, 4122, 4141, 4212, 4221, 4411, 8112, 8121, 8211

Offset: 1

Amarnath Murthy, May 03 2001

			124 is a term as the geometric mean of digits is (1*2*4) = 8 = 2^3.

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

Cf. A061427-A061430. A069512 gives another version.

Cf. A028846.

a061426 n = a061426_list !! (n-1)
a061426_list = g [1] where
   g ds = if product ds == 2 ^ 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

More terms from Erich Friedman, May 08 2001

A061427 Geometric mean of the digits = 3. In other words, the product of the digits is = 3^k where k is the number of digits.

Original entry on oeis.org

3, 19, 33, 91, 139, 193, 319, 333, 391, 913, 931, 1199, 1339, 1393, 1919, 1933, 1991, 3139, 3193, 3319, 3333, 3391, 3913, 3931, 9119, 9133, 9191, 9313, 9331, 9911, 11399, 11939, 11993, 13199, 13339, 13393, 13919, 13933, 13991, 19139, 19193

Offset: 1

Amarnath Murthy, May 03 2001

			319 is a term as the geometric mean of digits is (3*1*9) = 27 = 3^3.

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

Cf. A061426-A061430.

Cf. A174813.

a061427 n = a061427_list !! (n-1)
a061427_list = g [1] where
   g ds = if product ds == 3 ^ length ds
          then foldr (\d v -> 10 * v + d) 0 ds : g (s ds) else g (s ds)
   s [] = [1]; s (9:ds) = 1 : s ds; s (d:ds) = 3*d : ds
-- Reinhard Zumkeller, Jan 13 2014

Select[Range[20000],GeometricMean[IntegerDigits[#]]==3&] (* Harvey P. Dale, Dec 11 2011 *)

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

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.

Original entry on oeis.org

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

A061429 Geometric mean of the digits = 6. In other words, the product of the digits is = 6^k where k is the number of digits.

Original entry on oeis.org

6, 49, 66, 94, 389, 398, 469, 496, 649, 666, 694, 839, 893, 938, 946, 964, 983, 2899, 2989, 2998, 3689, 3698, 3869, 3896, 3968, 3986, 4499, 4669, 4696, 4949, 4966, 4994, 6389, 6398, 6469, 6496, 6649, 6666, 6694, 6839, 6893, 6938, 6946, 6964, 6983, 8299

Offset: 1

Amarnath Murthy, May 03 2001

The smallest number containing all the possible digits is 123468889999999. - Jianing Song, Nov 21 2019

			694 is a term as the geometric mean of digits is (6*9*4)^(1/3)= 6.

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

Cf. A061426-A061430.

Cf. A000400.

a061429 n = a061429_list !! (n-1)
a061429_list = filter (h 1 1) [1..] where
   h 0   = False
   h u v 0 = u == v
   h u v w = h (r * u) (6 * v) w' where (w', r) = divMod w 10
-- Reinhard Zumkeller, Jan 13 2014

Select[Range[9000],GeometricMean[IntegerDigits[#]]==6&] (* Harvey P. Dale, May 29 2021 *)

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

cp's OEIS Frontend

A285094 Corresponding values of geometric means of digits of numbers from A061430.

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A061426 Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digits.

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A061427 Geometric mean of the digits = 3. In other words, the product of the digits is = 3^k where k is the number of digits.

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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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A061429 Geometric mean of the digits = 6. In other words, the product of the digits is = 6^k where k is the number of digits.

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