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%I #18 Nov 10 2017 02:28:18
%S 0,1,11,101,111,1111,11011,11111,101101,111111,1010101,1011101,
%T 1110111,1111111,11111111,111101111,111111111,1101111011,1111111111,
%U 11011011011,11011111011,11111011111,11111111111,101101101101,111111111111,1011010101101,1011011101101,1111110111111,1111111111111
%N Recursive palindromes in base 2: palindromes n where each half of the digits of n is also a recursive palindrome.
%C 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 Lior Manor, <a href="/A240602/b240602.txt">Table of n, a(n) for n = 1..1000</a>
%e 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 FromDigits /@ Select[IntegerDigits[Range[2^12], 2], And[PalindromeQ@ Take[#, Floor[Length[#]/2]], PalindromeQ[#]] &] (* _Michael De Vlieger_, Nov 08 2017 *)
%Y Cf. A057148, A240601, A165785.
%K base,nonn
%O 1,3
%A _Lior Manor_, Apr 13 2014
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