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 A002516 #52 Sep 20 2021 04:38:27
%S A002516 0,3,6,2,12,7,4,10,24,11,14,18,8,15,20,26,48,19,22,34,28,23,36,42,16,
%T A002516 27,30,50,40,31,52,58,96,35,38,66,44,39,68,74,56,43,46,82,72,47,84,90,
%U A002516 32,51,54,98,60,55,100,106,80,59,62,114,104,63,116,122,192,67,70,130
%N A002516 Earliest sequence with a(a(n)) = 2n.
%H A002516 T. D. Noe, <a href="/A002516/b002516.txt">Table of n, a(n) for n = 0..1000</a>
%H A002516 Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H A002516 Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%H A002516 <a href="/index/Aa#aan">Index entries for sequences of the a(a(n)) = 2n family</a>
%F A002516 a(4n) = 2*(a(2n)), a(4n+1) = 4n+3, a(4n+2) = 2*(a(2n+1)), a(4n+3) = 8n+2. - _Henry Bottomley_, Apr 27 2000
%F A002516 From _Ralf Stephan_, Feb 22 2004: (Start)
%F A002516 a(n) = n + 2*A006519(n) if odd part of n is of form 4k+1, or 2n - 4*A006519(n) otherwise.
%F A002516 a(2n) = 2*a(n), a(2n+1) = 2n + 3 + (2n - 5)*[n mod 2].
%F A002516 G.f.: Sum_{k>=0} 2^k*t(6t^6 + t^4 + 2t^2 + 3)/(1 - t^4)^2, t = x^2^k. (End)
%t A002516 a[0] = 0; a[n_ /; Mod[n, 2] == 0] := a[n] = 2*a[n/2]; a[n_ /; Mod[n, 4] == 1] := n+2; a[n_ /; Mod[n, 4] == 3] := 2(n-2); Table[a[n], {n, 0, 67}] (* _Jean-François Alcover_, Feb 06 2012, after _Henry Bottomley_ *)
%o A002516 (PARI) v2(n)=valuation(n,2)
%o A002516 a(n)=2^v2(n)*(-1+3/2*n/2^v2(n)-(-3+1/2*n/2^v2(n))*(-1)^((n/2^v2(n)-1)/2))
%o A002516 (PARI) a(n)=local(t); if(n<1,0,if(n%2==0,2*a(n/2),t=(n-1)/2; 3*t+1/2-(t-5/2)*(-1)^t)) \\ _Ralf Stephan_, Feb 22 2004
%o A002516 (Haskell)
%o A002516 import Data.List (transpose)
%o A002516 a002516 n = a002516_list !! n
%o A002516 a002516_list = 0 : concat (transpose
%o A002516 [a004767_list, f a002516_list, a017089_list, g $ drop 2 a002516_list])
%o A002516 where f [z] = []; f (_:z:zs) = 2 * z : f zs
%o A002516 g [z] = [z]; g (z:_:zs) = 2 * z : g zs
%o A002516 -- _Reinhard Zumkeller_, Jun 08 2015
%Y A002516 Cf. A002517, A004767, A007379, A017089, A091067.
%K A002516 nonn,nice
%O A002516 0,2
%A A002516 _Colin Mallows_