%I #27 Jul 21 2018 15:53:20

%S 0,2,1,3,8,10,6,11,4,9,5,7,12,14,13,15,26,34,18,32,40,42,35,43,24,38,

%T 16,27,41,46,30,44,19,33,17,22,36,47,25,39,20,28,21,23,31,45,29,37,48,

%U 50,49,51,56,58,54,59,52,57,53,55,60,62,61,63,74,106,66

%N Lexicographically earliest sequence of distinct nonnegative numbers such that for any n >= 0, A065359(a(n)) = - A065359(n).

%C This sequence is a self-inverse permutation of the nonnegative numbers, with fixed points A039004.

%C We can build an analog of this sequence for any base b > 1 by considering the alternating sum of digits in base b instead of A065359.

%C This sequence has similarities with A298847.

%C The scatter plots have an interesting, "fibrous" look. - _Antti Karttunen_, Jul 21 2018

%H Rémy Sigrist, <a href="/A302544/b302544.txt">Table of n, a(n) for n = 0..16384</a>

%H Rémy Sigrist, <a href="/A302544/a302544.png">Colored scatterplot of the first 2^16 terms</a> (where the color is function of A065359(n))

%H Rémy Sigrist, <a href="/A302544/a302544_1.png">Scatterplot of the first 3^10 terms of the base 3 analog of this sequence</a>

%H Rémy Sigrist, <a href="/A302544/a302544_3.png">Scatterplot of the first 4^10 terms of the base 4 analog of this sequence</a>

%H Rémy Sigrist, <a href="/A302544/a302544_2.png">Scatterplot of the first 10^6 terms of the base 10 analog of this sequence</a>

%H Rémy Sigrist, <a href="/A302544/a302544_4.png">Scatterplot of the first 10!/2 terms of the factorial base analog of this sequence</a>

%H Rémy Sigrist, <a href="/A302544/a302544.txt">C++ program for A302544</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms, alongside the binary representations of n and of a(n), and A065359(n), are:

%e n a(n) bin(n) bin(a(n)) A065359(n)

%e -- ---- ------ --------- ----------

%e 0 0 0 0 0

%e 1 2 1 10 1

%e 2 1 10 1 -1

%e 3 3 11 11 0

%e 4 8 100 1000 1

%e 5 10 101 1010 2

%e 6 6 110 110 0

%e 7 11 111 1011 1

%e 8 4 1000 100 -1

%e 9 9 1001 1001 0

%e 10 5 1010 101 -2

%e 11 7 1011 111 -1

%e 12 12 1100 1100 0

%e 13 14 1101 1110 1

%e 14 13 1110 1101 -1

%e 15 15 1111 1111 0

%e 16 26 10000 11010 1

%e 17 34 10001 100010 2

%e 18 18 10010 10010 0

%e 19 32 10011 100000 1

%e 20 40 10100 101000 2

%o (C++) See Links section.

%Y Cf. A039004 (fixed points), A065359, A298847.

%K nonn,look,base

%O 0,2

%A _Rémy Sigrist_, Apr 09 2018