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A093684
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In binary representation: number of occurrences of n in n!.
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4
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1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 3, 0, 1, 0, 2, 0, 1, 1, 1, 1, 2, 3, 2, 2, 2, 1, 1, 1, 3, 0, 2, 1, 3, 1, 1, 0, 1, 2, 2, 3, 3, 1, 1, 1, 1, 2, 2, 4, 3, 3, 3, 2, 2, 0, 3, 1, 5, 5, 6, 4, 1, 5, 2, 3, 2, 2, 4, 1, 1, 1, 4, 1, 1, 1, 2, 3, 3, 4, 5, 0, 3, 2, 1, 4, 3, 4, 5, 3, 2, 1, 2, 3, 3, 3, 3, 6, 2, 3, 4, 4, 2
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OFFSET
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1,12
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COMMENTS
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LINKS
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EXAMPLE
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n=12->'1100', 12!=479001600->'11100100011001111110000000000' with three occurrences of '1100': '.1100....1100....1100........', therefore a(12)=3.
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MAPLE
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f:= proc(n) local L, Lf;
L:= convert(convert(n, binary), string);
Lf:= convert(convert(n!, binary), string);
nops([StringTools:-SearchAll(L, Lf)])
end proc:
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MATHEMATICA
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non[n_]:=Module[{b=IntegerDigits[n, 2], f=IntegerDigits[n!, 2]}, Length[ Select[ Partition[ f, Length[b], 1], #==b&]]]; Array[non, 110] (* Harvey P. Dale, Jun 04 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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