A175297 Convert n to binary. AND each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.

1, 0, 3, 0, 5, 2, 7, 0, 9, 0, 9, 0, 9, 6, 15, 0, 17, 0, 17, 4, 21, 4, 21, 0, 17, 10, 27, 4, 21, 14, 31, 0, 33, 0, 33, 0, 33, 0, 33, 0, 33, 0, 33, 12, 45, 12, 45, 0, 33, 18, 51, 0, 33, 18, 51, 0, 33, 18, 51, 12, 45, 30, 63, 0, 65, 0, 65, 0, 65, 0, 65, 8, 73, 8, 73, 8, 73, 8, 73, 0, 65, 0, 65

Offset: 1

Author

Leroy Quet, Mar 24 2010

Keywords

• base
• nonn

Comments

By "respective" digits of binary n and binary A030101(n), the rightmost digit of A030101(n) ( which is a 1) is AND'ed with the rightmost digit of n. A030101(n) is represented with the appropriate number of leading 0's.

Examples

			20 in binary is 10100. The reversal of the binary digits is 00101. So, from leftmost to rightmost respective digits, we AND 10100 and 00101: 1 AND 0 = 0. 0 AND 0 = 0. 1 AND 1 = 1. 0 AND 0 = 0. And 0 AND 1 = 1. So, 10100 AND 00101 is 100, which is 4 in decimal. So a(20) = 4.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030101, A175298.

Programs

Mathematica

Table[f = IntegerDigits[x, 2]; f = f + Reverse[f]; FromDigits[ Table[If[f[[r]] == 2, 1, 0], {r, 1, Length[f]}], 2], {x, 83}] (* Dylan Hamilton, Oct 15 2010 *)
Table[With[{d = IntegerDigits[n, 2]}, FromDigits[#, 2] &@ Map[BitAnd @@ # &, Transpose@{d, Reverse@ d}]], {n, 83}] (* Michael De Vlieger, Sep 03 2017 *)

Extensions

Extended, with redundant initial entries included, by Dylan Hamilton, Oct 15 2010