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A028846
Numbers whose product of digits is a power of 2.
17
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
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
CROSSREFS
KEYWORD
nonn,base
EXTENSIONS
More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
STATUS
approved