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A284324
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Numbers n such that product of digits of n is a power of 8.
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5
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1, 8, 11, 18, 24, 42, 81, 88, 111, 118, 124, 142, 181, 188, 214, 222, 241, 248, 284, 412, 421, 428, 444, 482, 811, 818, 824, 842, 881, 888, 1111, 1118, 1124, 1142, 1181, 1188, 1214, 1222, 1241, 1248, 1284, 1412, 1421, 1428, 1444, 1482, 1811, 1818, 1824, 1842
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OFFSET
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1,2
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COMMENTS
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There are (2 + 4^d)/3 terms with d digits, for each d >= 1. - Robert Israel, Mar 31 2017
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LINKS
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EXAMPLE
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1111 is in the sequence because 1*1*1*1 = 1 = 8^0.
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MAPLE
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dmax:= 4: # to get all terms with at most dmax digits
B[0, 1]:= {1, 8}:
B[1, 1]:= {2}:
B[2, 1]:= {4}:
for d from 2 to dmax do
for j from 0 to 2 do
B[j, d]:= map(t -> (10*t+1, 10*t+8), B[j, d-1])
union map(t -> 10*t+4, B[(j+1) mod 3, d-1])
union map(t->10*t+2, B[(j+2) mod 3, d-1])
od od:
seq(op(sort(convert(B[0, d], list))), d=1..dmax); # Robert Israel, Mar 31 2017
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PROG
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(Magma) Set(Sort([n: n in [1..10000], k in [0..20] | &*Intseq(n) eq 8^k]))
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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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STATUS
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approved
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