A165785 -id:A165785 - cp's OEIS frontend

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

Lior Manor, Apr 13 2014

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.

			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).

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

Cf. A057148, A240601, A165785.

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

A165784 a(1)=1. For n >= 2, each a(n) = the decimal equivalent of either a(k)U0Ua(k) or a(k)U1Ua(k), where U denotes concatenation of the binary representations of the arguments, and where k is some positive integer < n. The numbers are arranged in numerical order.

Original entry on oeis.org

1, 5, 7, 85, 93, 119, 127, 21845, 21973, 23901, 24029, 30583, 30711, 32639, 32767, 1431655765, 1431688533, 1440044501, 1440077269, 1566399837, 1566432605, 1574788573, 1574821341, 2004318071, 2004350839, 2012706807, 2012739575

Offset: 1

Leroy Quet, Sep 26 2009

Each term is a palindrome when written in base 2.

Cf. A165785

More terms from Sean A. Irvine, Dec 03 2009

cp's OEIS Frontend

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

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