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%I #10 Aug 05 2022 15:36:04
%S 0,1,2,3,4,5,6,7,8,17,10,11,12,13,14,15,19,9,18,16,20,21,51,44,24,38,
%T 26,32,28,45,46,31,27,33,34,35,36,48,25,39,40,49,53,43,23,29,30,47,37,
%U 41,50,22,52,42,54,55,140,133,58,106,115,79,62,113,127,99
%N Bit-reverse the odd part of the negaFibonacci representation of n: a(n) = A356327(A057889(A215024(n))).
%C This sequence is a self-inverse permutation of the nonnegative integers similar to A343150, A344682, A345201 and A356332.
%H Rémy Sigrist, <a href="/A356331/b356331.txt">Table of n, a(n) for n = 0..6765</a>
%H Rémy Sigrist, <a href="/A356331/a356331.gp.txt">PARI program</a>
%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(a(n)) = n.
%F a(n) <= A000045(2*k) iff n <= A000045(2*k).
%e The first terms, alongside the corresponding negaFibonacci representations, are:
%e n a(n) nega(n) nega(a(n))
%e -- ---- ------- ----------
%e 0 0 0 0
%e 1 1 1 1
%e 2 2 100 100
%e 3 3 101 101
%e 4 4 10010 10010
%e 5 5 10000 10000
%e 6 6 10001 10001
%e 7 7 10100 10100
%e 8 8 10101 10101
%e 9 17 1001010 1010010
%e 10 10 1001000 1001000
%e 11 11 1001001 1001001
%e 12 12 1000010 1000010
%e 13 13 1000000 1000000
%e 14 14 1000001 1000001
%e 15 15 1000100 1000100
%e 16 19 1000101 1010001
%e 17 9 1010010 1001010
%e 18 18 1010000 1010000
%e 19 16 1010001 1000101
%e 20 20 1010100 1010100
%e 21 21 1010101 1010101
%o (PARI) See Links section.
%Y Cf. A000045, A057889, A215025, A343150, A344682, A345201, A356327, A356332.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Aug 04 2022