A028846 Numbers whose product of digits is a power of 2.

1, 2, 4, 8, 11, 12, 14, 18, 21, 22, 24, 28, 41, 42, 44, 48, 81, 82, 84, 88, 111, 112, 114, 118, 121, 122, 124, 128, 141, 142, 144, 148, 181, 182, 184, 188, 211, 212, 214, 218, 221, 222, 224, 228, 241, 242, 244, 248, 281, 282, 284, 288, 411, 412, 414, 418, 421, 422, 424, 428, 441, 442, 444, 448

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

Numbers using only digits 1, 2, 4, and 8. - Michel Lagneau, Dec 01 2010

Examples

			28 is in the sequence because 2*8 = 2^4. - _Michel Lagneau_, Dec 01 2010
		

Links

• Bo Gyu Jeong, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A007954, A028889, A028838.

Cf. A174813, A061426.

Programs

Haskell

a028846 n = a028846_list !! (n-1)
a028846_list = f [1] where
   f ds = foldr (\d v -> 10 * v + d) 0 ds : f (s ds)
   s [] = [1]; s (8:ds) = 1 : s ds; s (d:ds) = 2*d : ds
-- Reinhard Zumkeller, Jan 13 2014

Mathematica

Select[Range[1000], IntegerQ[Log[2, Times @@ (IntegerDigits[#])]] &] (* Michel Lagneau, Dec 01 2010 *)

PARI

is(n)=#setminus(Set(digits(n)), [1,2,4,8])==0 \\ Charles R Greathouse IV, Apr 24 2025

Python

from itertools import count, islice, product
def agen(): yield from (int("".join(p)) for d in count(1) for p in product("1248", repeat=d))
print(list(islice(agen(), 64))) # Michael S. Branicky, Aug 21 2022

Python

def A028846(n):
    m = (k:=3*n+1).bit_length()-1>>1
    return sum(10**j<<((k-(1<<(m<<1)))//(3<<(j<<1))&3) for j in range(m)) # Chai Wah Wu, Jun 28 2025

Formula

Given a(0) = 0 and n = 4k - r, where 0 <= r <= 3, a(n) = 10*a(k-1) + 2^(3-r). - Clinton H. Dan, Aug 21 2022

Extensions

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)