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 A335115 #16 Dec 02 2020 03:17:19
%S A335115 1,1,3,3,5,3,7,5,9,5,11,9,13,7,15,11,17,9,19,15,21,11,23,15,25,13,27,
%T A335115 21,29,15,31,21,33,17,35,27,37,19,39,25,41,21,43,33,45,23,47,33,49,25,
%U A335115 51,39,53,27,55,35,57,29,59,45,61,31,63,43,65,33,67,51,69,35,71,45,73,37,75
%N A335115 a(2*n) = 2*n - a(n), a(2*n+1) = 2*n + 1.
%H A335115 Amiram Eldar, <a href="/A335115/b335115.txt">Table of n, a(n) for n = 1..10000</a>
%F A335115 G.f.: Sum_{k>=0} (-1)^k * x^(2^k) / (1 - x^(2^k))^2.
%F A335115 G.f. A(x) satisfies: A(x) = x / (1 - x)^2 - A(x^2).
%F A335115 Dirichlet g.f.: zeta(s-1) / (1 + 2^(-s)).
%F A335115 a(n) = Sum_{d|n} A154269(n/d) * d.
%F A335115 Sum_{k=1..n} a(k) ~ 2*n^2/5. - _Vaclav Kotesovec_, Jun 11 2020
%F A335115 Multiplicative with a(2^e) = A001045(e+1) and a(p^e) = p^e for e >= 0 and prime p > 2. - _Werner Schulte_, Oct 05 2020
%t A335115 a[n_] := a[n] = If[EvenQ[n], n - a[n/2], n]; Table[a[n], {n, 1, 75}]
%t A335115 nmax = 75; CoefficientList[Series[Sum[(-1)^k x^(2^k)/(1 - x^(2^k))^2, {k, 0, Floor[Log[2, nmax]]}], {x, 0, nmax}], x] // Rest
%t A335115 f[p_, e_] := If[p == 2, (2^(e + 1) + (-1)^e)/3, p^e]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Dec 02 2020 *)
%o A335115 (PARI) a(n) = my(k=valuation(n,2)); (n<<1 + (n>>k)*(-1)^k)/3; \\ _Kevin Ryde_, Oct 06 2020
%Y A335115 Cf. A035263, A050292, A129527, A154269, A001045.
%K A335115 nonn,mult
%O A335115 1,3
%A A335115 _Ilya Gutkovskiy_, May 23 2020