A152221 a(n) = the largest integer k where the binary representations of both k and of k+1 occur as substrings in the binary representation of n. a(n) = 0 if n = 2^m -1, for m = any positive integer.

0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 2, 3, 5, 6, 0, 1, 1, 1, 3, 4, 1, 5, 2, 3, 3, 5, 5, 6, 13, 14, 0, 1, 1, 1, 3, 1, 4, 3, 3, 4, 9, 1, 10, 11, 5, 6, 2, 3, 3, 3, 3, 5, 5, 5, 6, 7, 6, 13, 13, 14, 29, 30, 0, 1, 1, 1, 3, 1, 4, 3, 7, 8, 1, 9, 4, 3, 5, 6, 3, 4, 4, 9, 19, 20, 1, 21, 10, 11, 11, 10, 5, 11, 13, 14, 2, 3

Offset

1,6

Comments

If n = 2^m -1, then there is no pair of consecutive positive integers that, when represented in binary, occur as substrings in the binary representation of n. For n = any positive integer not of the form 2^m -1, there is always at least one positive integer k such that the binary representations of both k and k+1 occur as substrings in the binary representation of n.

Links

Table of n, a(n) for n=1..96.

Example

12 represented in binary is 1100. a(12) = 3 because the binary representation of 3 (which is 11) occurs in 1100 (like so: (11)00), the binary representation of 4 (which is 100) occurs in 1100 (like so: 1(100)) and no larger pair of consecutive integers occurs within 1100.

Crossrefs

A152222

Sequence in context: A124737 A121303 A166396 * A144092 A333467 A120648

Adjacent sequences: A152218 A152219 A152220 * A152222 A152223 A152224

Keyword

base,nonn

Author

Leroy Quet, Nov 29 2008

Extensions

Extended by Ray Chandler, Dec 05 2008

Status

approved