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

1,2

Comments

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

Links

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007954, A028889, A028838.

Cf. A174813, A061426.

Sequence in context: A028889 A235700 A174781 * A274924 A080152 A136994

Adjacent sequences: A028843 A028844 A028845 * A028847 A028848 A028849

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved