cp's OEIS Frontend

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.

%I A175297 #16 Sep 04 2017 04:31:36
%S A175297 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,
%T A175297 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,
%U A175297 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
%N 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.
%C A175297 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.
%H A175297 Michael De Vlieger, <a href="/A175297/b175297.txt">Table of n, a(n) for n = 1..10000</a>
%e A175297 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.
%t A175297 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 *)
%t A175297 Table[With[{d = IntegerDigits[n, 2]}, FromDigits[#, 2] &@ Map[BitAnd @@ # &, Transpose@{d, Reverse@ d}]], {n, 83}] (* _Michael De Vlieger_, Sep 03 2017 *)
%Y A175297 Cf. A030101, A175298.
%K A175297 base,nonn
%O A175297 1,3
%A A175297 _Leroy Quet_, Mar 24 2010
%E A175297 Extended, with redundant initial entries included, by _Dylan Hamilton_, Oct 15 2010