A175267 a(n) = the minimum number of 0's that, if removed from the binary representation of n, leaves a palindrome.

0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 1, 2, 1, 1, 0, 4, 0, 1, 2, 2, 0, 2, 1, 3, 2, 2, 0, 2, 1, 1, 0, 5, 0, 1, 3, 2, 1, 3, 2, 3, 1, 1, 1, 3, 0, 2, 1, 4, 3, 3, 0, 3, 1, 1, 1, 3, 2, 2, 1, 2, 1, 1, 0, 6, 0, 1, 4, 2, 2, 4, 3, 3, 0, 2, 2, 4, 1, 3, 2, 4, 2, 2, 1, 2, 0, 2, 2, 4, 1, 1, 2, 3, 0, 2, 1, 5, 4, 4, 0, 4, 1, 1, 2, 4

Offset

0,5

Comments

a(2^m) = m, for all m >= 0.

a(2^m-1) = 0 for all m >= 0.

If 2^k is the largest power of 2 that divides n, then a(n) >= k.

Links

Table of n, a(n) for n=0..104.

Example

20 in binary is 10100. This is not a palindrome, so a(20) > 0. Removing one 0 gets either 1100 or 1010 (the latter in two ways). Neither of these is a palindrome, so a(20)>1. But removing the last two 0's so that we have 101 does indeed leave a palindrome. So a(20) = 2.

Crossrefs

Sequence in context: A060689 A053119 A162515 * A108045 A374700 A298972

Adjacent sequences: A175264 A175265 A175266 * A175268 A175269 A175270

Keyword

base,nonn

Author

Leroy Quet, Mar 18 2010

Extensions

Extended by D. S. McNeil, May 10 2010

Status

approved