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 A132680 #12 Feb 16 2025 08:33:06 %S A132680 1,1,1,3,1,3,3,3,1,3,3,3,3,3,3,5,1,3,3,3,3,3,3,5,3,3,3,5,3,5,5,5,1,3, %T A132680 3,3,3,3,3,5,3,3,3,5,3,5,5,5,3,3,3,5,3,5,5,5,3,5,5,5,5,5,5,7,1,3,3,3, %U A132680 3,3,3,5,3,3,3,5,3,5,5,5,3,3,3,5,3,5,5,5,3,5,5,5,5,5,5,7,3,3,3,5,3,5,5,5,3 %N A132680 Number of ones in binary representation of odious numbers. %H A132680 Reinhard Zumkeller, <a href="/A132680/b132680.txt">Table of n, a(n) for n = 1..10001</a> %H A132680 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OdiousNumber.html">Odious Number</a>. %H A132680 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Thue-MorseSequence.html">Thue-Morse Sequence</a>. %H A132680 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>. %F A132680 a(n) = a(floor(n/2)) + 2*(n mod 2)*(1-A010060(n)). %F A132680 a(n) = A000120(A000069(n)). %F A132680 a(A129771(n)) = a((A129771(n)-1)/2) + 2. %F A132680 a(A083420(n)) = A005408(n). %t A132680 Select[DigitCount[Range[200], 2, 1], OddQ] (* _Amiram Eldar_, Jul 22 2023 *) %o A132680 (PARI) a(n)=hammingweight(2*n-1-hammingweight(n-1)%2) \\ _Charles R Greathouse IV_, Mar 26 2013 %Y A132680 Cf. A000069, A000120, A010060, A005408, A083420, A129771. %K A132680 nonn,easy %O A132680 1,4 %A A132680 _Reinhard Zumkeller_, Aug 26 2007