

A242869


Largest integer m < n having a binary expansion that is a prefix and a suffix of the binary expansion of n; a(0)=0.


5



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

0,8


COMMENTS

The prefix and the suffix are allowed to overlap.
a(n) <= A147755(n).
a(2^n) = 0.
a(2^n1) = 2^(n1)1 for n>0.
a(n) = 0 iff n in { A091065 }.
a(n) > 1 iff n in { A091066 }.
A029837(a(n)+1) = A091064(n).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..8192


EXAMPLE

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.


MAPLE

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);


CROSSREFS

Cf. A147755.
Sequence in context: A097610 A161556 A317302 * A224878 A129555 A147755
Adjacent sequences: A242866 A242867 A242868 * A242870 A242871 A242872


KEYWORD

nonn,base,look


AUTHOR

Alois P. Heinz, May 24 2014


STATUS

approved



