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

1,3

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.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A030101, A175298.

Sequence in context: A159980 A343054 A098496 * A165754 A193067 A177886

Adjacent sequences: A175294 A175295 A175296 * A175298 A175299 A175300

Keyword

base,nonn

Author

Leroy Quet, Mar 24 2010

Extensions

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

Status

approved