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
Examples
248 is a term as the geometric mean of digits is (2*4*8) = 64 = 4^3.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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Haskell
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 -
Python
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
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001