A298475 - OEIS

%I #15 Jan 30 2018 21:14:44

%S 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,

%T 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,

%U 3,3,2,2,1,2,3,2,2,3,2,2,3,2,3,2,1

%N Minimal size of a palindromic partition of the binary representation of n.

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

%H Peter Kagey, <a href="/A298475/b298475.txt">Table of n, a(n) for n = 1..10000</a>

%e The following table shows the partitions of binary representations of n into a(n) palindromes:

%e n   | a(n) | binary   | partition

%e ----+------+----------+-----------------

%e 5   | 1    | 101      | (101)

%e 6   | 2    | 110      | (11)(0)

%e 7   | 1    | 111      | (111)

%e 13  | 2    | 1101     | (1)(101)

%e 37  | 3    | 100101   | (1001)(0)(1)

%e 203 | 4    | 11001011 | (11)(00)(101)(1)

%t {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 *)

%Y Cf. A006995, A298474.

%K nonn,base

%O 1,2

%A _Peter Kagey_, Jan 19 2018