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A028846
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Numbers whose product of digits is a power of 2.
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17
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Numbers using only digits 1, 2, 4, and 8. - Michel Lagneau, Dec 01 2010
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LINKS
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FORMULA
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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
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EXAMPLE
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28 is in the sequence because 2*8 = 2^4. - Michel Lagneau, Dec 01 2010
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MATHEMATICA
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Select[Range[1000], IntegerQ[Log[2, Times @@ (IntegerDigits[#])]] &] (* Michel Lagneau, Dec 01 2010 *)
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PROG
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(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
(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))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
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STATUS
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approved
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