This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A240602 #18 Nov 10 2017 02:28:18 %S A240602 0,1,11,101,111,1111,11011,11111,101101,111111,1010101,1011101, %T A240602 1110111,1111111,11111111,111101111,111111111,1101111011,1111111111, %U A240602 11011011011,11011111011,11111011111,11111111111,101101101101,111111111111,1011010101101,1011011101101,1111110111111,1111111111111 %N A240602 Recursive palindromes in base 2: palindromes n where each half of the digits of n is also a recursive palindrome. %C A240602 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. %H A240602 Lior Manor, <a href="/A240602/b240602.txt">Table of n, a(n) for n = 1..1000</a> %e A240602 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). %t A240602 FromDigits /@ Select[IntegerDigits[Range[2^12], 2], And[PalindromeQ@ Take[#, Floor[Length[#]/2]], PalindromeQ[#]] &] (* _Michael De Vlieger_, Nov 08 2017 *) %Y A240602 Cf. A057148, A240601, A165785. %K A240602 base,nonn %O A240602 1,3 %A A240602 _Lior Manor_, Apr 13 2014