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.

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, 107, 27, 231, 93, 189, 31, 65, 33, 273, 99, 73, 165, 153, 231, 325, 165, 85, 107, 717, 45, 93, 189, 195, 99, 403, 51, 843, 107, 219, 119, 455, 231, 471, 119, 633, 189, 381, 63

Offset: 1

Author

Leroy Quet, Oct 19 2008

Keywords

• base
• nonn

Comments

For n is a power of 2 (A000079), a(n) = 2*n + 1.

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.

a(A006995(n)) = A006995(n). - Ray Chandler, Oct 26 2008

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1024

Crossrefs

Cf. A000079, A006995, A145799

Programs

Mathematica

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 *)

Extensions

Extended by Ray Chandler, Oct 26 2008