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 A145800 #16 Aug 27 2022 03:13:10
%S A145800 1,5,3,9,5,27,7,17,9,21,27,51,27,93,15,33,17,73,51,165,21,45,93,99,51,
%T A145800 107,27,231,93,189,31,65,33,273,99,73,165,153,231,325,165,85,107,717,
%U A145800 45,93,189,195,99,403,51,843,107,219,119,455,231,471,119,633,189,381,63
%N A145800 a(n) = the smallest positive integer that is an (odd) palindrome when represented in binary and that contains within it the binary representation of n.
%C A145800 For n is a power of 2 (A000079), a(n) = 2*n + 1.
%C A145800 This sequence contains, by definition, those binary palindromes that are odd, i.e., those palindromes without leading zeros. In other words, only integers occurring in sequence A006995 occur in this sequence.
%C A145800 a(A006995(n)) = A006995(n). - _Ray Chandler_, Oct 26 2008
%H A145800 Michael De Vlieger, <a href="/A145800/b145800.txt">Table of n, a(n) for n = 1..1024</a>
%e A145800 6 in binary is 110. Those integers which contain 110 in their binary representations are 6 (110 in binary), 12 (1100 in binary), 13 (1101 in binary), 14 (1110 in binary), 22 (10110 in binary), 24 (11000 in binary), 25 (11001 in binary), 26 (11010 in binary), 27 (11011 in binary), etc... Now, 27 (11011 in binary) is the smallest of these integers that is a binary palindrome; so a(6) = 27.
%t A145800 Table[With[{d = IntegerDigits[n, 2]}, k = 1; While[Nand[SequenceCount[Set[m, IntegerDigits[k, 2]], d] > 0, PalindromeQ@ m], k += 2]; k], {n, 63}] (* _Michael De Vlieger_, Oct 30 2017 *)
%Y A145800 Cf. A000079, A006995, A145799
%K A145800 base,nonn
%O A145800 1,2
%A A145800 _Leroy Quet_, Oct 19 2008
%E A145800 Extended by _Ray Chandler_, Oct 26 2008