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 A350091 #97 Dec 09 2024 01:56:10
%S A350091 0,1,0,3,4,5,1,7,8,9,0,11,12,13,3,15,16,17,4,19,20,21,5,23,24,25,1,27,
%T A350091 28,29,7,31,32,33,8,35,36,37,9,39,40,41,0,43,44,45,11,47,48,49,12,51,
%U A350091 52,53,13,55,56,57,3,59,60,61,15,63,64,65,16,67,68,69,17,71,72,73
%N A350091 a(n) = a(floor(n/4)) for n == 2 (mod 4), otherwise n.
%C A350091 a(n) deletes any trailing '10' bit pairs from n. So in base 4, it removes all trailing '2' digits.
%H A350091 Amiram Eldar, <a href="/A350091/b350091.txt">Table of n, a(n) for n = 0..10000</a>
%F A350091 A139391(2*a(n)+1) = A139391(2*n+1).
%F A350091 Sum_{k=1..n} a(k) ~ 2 * n^2 / 5. - _Amiram Eldar_, Aug 30 2024
%F A350091 a(n) = (A347840(n+1) - 1)/2. - _Alan Michael Gómez Calderón_, Dec 08 2024
%e A350091 Numbers between '' are in base 2: '0'->'0', so a(0)=0. '110'->'1', so a(6)=1. '1010'->'10' -> '0', so a(10)=0. a(floor((2^1000001)/3))=0.
%t A350091 a[n_] := a[n] = If[Mod[n, 4] == 2, a[(n - 2)/4], n]; Array[a, 100, 0] (* _Amiram Eldar_, Dec 14 2021 *)
%o A350091 (PARI) a(n) = if(2!=(n%4), n, my(m=3*n+2); m=m/4^valuation(m,4);(m+1)/3-1)
%Y A350091 Cf. A006519, A139391, A001511, A065883 (chop trailing 00 bit pairs), A347840.
%K A350091 nonn,easy
%O A350091 0,4
%A A350091 _Ruud H.G. van Tol_, Dec 14 2021