A298475 Minimal size of a palindromic partition of the binary representation of n.

1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 3, 1, 2, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 3, 3, 2, 2, 1, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 1

Offset

1,2

Comments

A palindromic partition of "xxoxoxxox" is (x)(xoxox)(xox).

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Example

The following table shows the partitions of binary representations of n into a(n) palindromes:
n   | a(n) | binary   | partition
----+------+----------+-----------------
5   | 1    | 101      | (101)
6   | 2    | 110      | (11)(0)
7   | 1    | 111      | (111)
13  | 2    | 1101     | (1)(101)
37  | 3    | 100101   | (1001)(0)(1)
203 | 4    | 11001011 | (11)(00)(101)(1)

Mathematica

{1, 2}~Join~Array[Function[w, Min@ Map[Length, Select[#, And[AllTrue[#, PalindromeQ], Union@ Map[Length, #] != {1}] &]] &@ Union@ Map[Select[SplitBy[#, IntegerQ], IntegerQ@ First@ # &] &, Map[Insert[w, ".", #] &, Map[{#} &, Rest@ Subsets@ Range@ Length@ w, {2}]]]]@ IntegerDigits[#, 2] &, 103, 3] (* Michael De Vlieger, Jan 23 2018 *)

Crossrefs

Cf. A006995, A298474.

Sequence in context: A321469 A365460 A235644 * A175096 A111627 A008618

Adjacent sequences: A298472 A298473 A298474 * A298476 A298477 A298478

Keyword

nonn,base

Author

Peter Kagey, Jan 19 2018

Status

approved