A240602 Recursive palindromes in base 2: palindromes n where each half of the digits of n is also a recursive palindrome.

0, 1, 11, 101, 111, 1111, 11011, 11111, 101101, 111111, 1010101, 1011101, 1110111, 1111111, 11111111, 111101111, 111111111, 1101111011, 1111111111, 11011011011, 11011111011, 11111011111, 11111111111, 101101101101, 111111111111, 1011010101101, 1011011101101, 1111110111111, 1111111111111

Offset: 1

Author

Lior Manor, Apr 13 2014

Keywords

• base
• nonn

Comments

A number n with m digits in base 2 is a member of a(n) if n is a palindrome, and the first floor(m/2) digits of n is already a previous term of a(n). Fast generation of new terms with 2m digits can be done by concatenating the previous terms with m digits twice. Fast generation of new terms with 2m+1 digits can be done by concatenating the previous terms with m digits twice with any single digit in the middle. The smallest palindrome which is not a member of a(n) is 1001.

Examples

			11011 is in the sequence since it is a palindrome of 5 digits, and the first floor(5/2) digits of it, 11, is also a term. 1001 and 10001 are not in a(n) since 10 is not in a(n).
		

Links

• Lior Manor, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A057148, A240601, A165785.

Programs

Mathematica

FromDigits /@ Select[IntegerDigits[Range[2^12], 2], And[PalindromeQ@ Take[#, Floor[Length[#]/2]], PalindromeQ[#]] &] (* Michael De Vlieger, Nov 08 2017 *)