%I #31 Apr 11 2024 10:37:46
%S 0,1,2,3,6,5,4,7,14,13,10,11,12,9,8,15,30,29,26,27,22,21,20,25,28,23,
%T 18,19,24,17,16,31,62,61,58,59,54,53,52,57,50,45,42,43,46,41,44,55,60,
%U 51,40,49,38,37,36,47,56,39,34,35,48,33,32,63,126,125,122
%N Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and of a(n) have the same length (A070939) and the same number of runs of consecutive equals digits (A005811).
%C This sequence is a self-inverse permutation of the nonnegative integers with infinitely many fixed points (for example, all terms of A000225 are fixed points).
%H Rémy Sigrist, <a href="/A371343/b371343.txt">Table of n, a(n) for n = 0..8191</a>
%H Rémy Sigrist, <a href="/A371343/a371343.png">Colored scatterplot of the first 2^20 terms</a> (where the color is function of A005811(n))
%H Rémy Sigrist, <a href="/A371343/a371343.gp.txt">PARI program</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The first terms, in decimal and in binary, are:
%e n a(n) bin(n) bin(a(n))
%e -- ---- ------ ---------
%e 0 0
%e 1 1 1 1
%e 2 2 10 10
%e 3 3 11 11
%e 4 6 100 110
%e 5 5 101 101
%e 6 4 110 100
%e 7 7 111 111
%e 8 14 1000 1110
%e 9 13 1001 1101
%e 10 10 1010 1010
%e 11 11 1011 1011
%e 12 12 1100 1100
%e 13 9 1101 1001
%e 14 8 1110 1000
%e 15 15 1111 1111
%o (PARI) \\ See Links section.
%Y See A331274 and A337242 for similar sequences.
%Y Cf. A000225, A005811, A070939.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Mar 24 2024