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.

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

Offset: 0

Author

Alois P. Heinz, May 24 2014

Keywords

• nonn
• base
• look

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).

Examples

			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.
		

Links

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

Crossrefs

Cf. A147755.

Programs

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);