A302544 - OEIS

%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