cp's OEIS Frontend

A161501 a(n) is the smallest positive integer that is a palindrome when represented in binary, and is made by appending some number (zero or more) of binary digits on the right of n's binary representation.

%I A161501 #20 Aug 27 2021 13:05:24
%S A161501 1,5,3,9,5,27,7,17,9,21,45,51,27,119,15,33,17,73,153,165,21,45,93,99,
%T A161501 51,107,27,231,119,495,31,65,33,273,561,73,297,153,313,325,165,85,693,
%U A161501 717,45,93,189,195,99,403,51,843,107,219,443,455,231,471,119,975,495,2015
%N A161501 a(n) is the smallest positive integer that is a palindrome when represented in binary, and is made by appending some number (zero or more) of binary digits on the right of n's binary representation.
%H A161501 Rémy Sigrist, <a href="/A161501/b161501.txt">Table of n, a(n) for n = 1..8192</a>
%e A161501 11 (decimal) in binary is 1011. Appending 01 to the right side of 1011 forms the binary palindrome 101101, which is 45 in decimal. Since two binary digits is the smallest number of digits that need to be appended to form a palindrome, then a(11) = 45. (Note that 45 is not the smallest positive number that when represented in binary is a palindrome and contains 1011 as a substring. That would instead be 11011 {binary} = 27 {decimal}.)
%o A161501 (PARI) a(n, base=2) = { my (b=digits(n, base)); if (b==Vecrev(b), return (n), my (t=[]); for (k=1, #b, t=concat(b[k],t); my (bt=concat(b,t)); if (bt==Vecrev(bt), return (fromdigits(bt, base))))) } \\ _Rémy Sigrist_, Mar 22 2020
%o A161501 (Python)
%o A161501 def A161501(n):
%o A161501     s = bin(n)[2:]
%o A161501     if s == s[::-1]:
%o A161501         return n
%o A161501     for i in range(1,len(s)):
%o A161501         if s[i:] == s[-1:i-1:-1]:
%o A161501             return int(s+s[i-1::-1],2) # _Chai Wah Wu_, Aug 27 2021
%Y A161501 Cf. A006995, A082216 (decimal variant), A145800, A161502.
%K A161501 base,nonn
%O A161501 1,2
%A A161501 _Leroy Quet_, Jun 11 2009
%E A161501 More terms from _Sean A. Irvine_, Sep 27 2009