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 A105081 #26 Jun 30 2022 08:38:23
%S A105081 1,2,4,3,7,8,6,5,13,14,16,15,11,12,10,9,25,26,28,27,31,32,30,29,21,22,
%T A105081 24,23,19,20,18,17,49,50,52,51,55,56,54,53,61,62,64,63,59,60,58,57,41,
%U A105081 42,44,43,47,48,46,45,37,38,40,39,35,36,34,33,97,98,100,99,103,104,102
%N A105081 a(n) = 1 + A003188(n - 1), n >= 1.
%C A105081 A permutation of the natural numbers.
%H A105081 Ivan Neretin, <a href="/A105081/b105081.txt">Table of n, a(n) for n = 1..8192</a>
%H A105081 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A105081 a(1) = 1, a(2^k + j) = 2^k + a(2^k - j + 1) for 1 <= j <= 2^k.
%F A105081 A000069(a(n)) = A065621(n).
%F A105081 As a composition of related permutations:
%F A105081 a(n) = A268718(A003188(n)). - _Antti Karttunen_, Feb 14 2016
%t A105081 Nest[Join[#,Length[#]+Reverse[#]]&,{1},7] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2012 *)
%o A105081 (Scheme) (define (A105081 n) (+ 1 (A003188 (- n 1)))) ;; _Antti Karttunen_, Feb 14 2016
%o A105081 (Python)
%o A105081 def A105081(n): return 1+(n-1^ n-1>>1) # _Chai Wah Wu_, Jun 29 2022
%Y A105081 Inverse permutation: A066194.
%Y A105081 Cf. A000069, A003188, A065621, A268718.
%K A105081 nonn,easy,look
%O A105081 1,2
%A A105081 _Philippe Deléham_, Apr 28 2005