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 A356759 #20 Aug 29 2022 10:28:41
%S A356759 0,1,2,3,4,5,6,7,9,8,10,11,12,15,17,13,16,14,18,19,20,25,22,28,30,21,
%T A356759 26,29,23,27,24,31,32,33,41,46,36,43,38,49,51,34,42,37,47,50,35,44,48,
%U A356759 39,45,40,52,53,54,67,59,75,80,56,70,77,62,72,64,83,85,55
%N A356759 Bit-reverse the odd part of the dual Zeckendorf representation of n: a(n) = A022290(A057889(A003754(n+1))).
%C A356759 This sequence is a self-inverse permutation of the nonnegative integers, similar to A345201 and A356331.
%C A356759 The dual Zeckendorf (or lazy Fibonacci) representation expresses uniquely a number n as a sum of distinct positive Fibonacci numbers; these distinct Fibonacci numbers can be encoded in binary, and the corresponding binary encoding, A003754(n+1), cannot have two consecutive nonleading 0's.
%H A356759 Rémy Sigrist, <a href="/A356759/b356759.txt">Table of n, a(n) for n = 0..10945</a>
%H A356759 Rémy Sigrist, <a href="/A356759/a356759.gp.txt">PARI program</a>
%H A356759 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%H A356759 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A356759 a(a(n)) = n.
%F A356759 a(n) < A000045(k) iff n < A000045(k).
%e A356759 For n = 49:
%e A356759 - the dual Zeckendorf representation of 49 is "1111010",
%e A356759 - reversing its odd part ("111101"), we obtain "1011110",
%e A356759 - so a(49) = 39.
%o A356759 (PARI) See Links section.
%Y A356759 Cf. A000045, A003714, A003754, A022290, A057889, A104326, A345201, A356331.
%K A356759 nonn,base,look
%O A356759 0,3
%A A356759 _Rémy Sigrist_, Aug 26 2022