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A242869
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Largest integer m < n having a binary expansion that is a prefix and a suffix of the binary expansion of n; a(0)=0.
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5
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0, 0, 0, 1, 0, 1, 0, 3, 0, 1, 2, 1, 0, 1, 0, 7, 0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 0, 3, 0, 1, 0, 15, 0, 1, 2, 1, 4, 1, 2, 1, 0, 1, 10, 1, 0, 5, 2, 1, 0, 1, 0, 3, 0, 1, 6, 3, 0, 1, 0, 3, 0, 1, 0, 31, 0, 1, 2, 1, 4, 1, 2, 1, 0, 9, 2, 1, 4, 1, 2, 1, 0, 1, 2, 1, 0, 21
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OFFSET
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0,8
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COMMENTS
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The prefix and the suffix are allowed to overlap.
a(2^n) = 0.
a(2^n-1) = 2^(n-1)-1 for n>0.
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LINKS
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EXAMPLE
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a(91) = 11 because 91 = (1011)011_2 = 101(1011)_2 and 11 = 1011_2.
a(84) = 0 because 84 = 1010100_2, only the empty bitstring is a proper prefix and suffix.
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MAPLE
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a:= proc(n) local m; m:=n;
while m>1 do m:= iquo(m, 2);
if m=irem(n, 2^(1+ilog2(m))) then return m fi
od; 0
end:
seq(a(n), n=0..100);
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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