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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).
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%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