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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

The prefix and the suffix are allowed to overlap.

a(n) <= A147755(n).

a(2^n) = 0.

a(2^n-1) = 2^(n-1)-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

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)