cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A302544 Lexicographically earliest sequence of distinct nonnegative numbers such that for any n >= 0, A065359(a(n)) = - A065359(n).

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%I A302544 #27 Jul 21 2018 15:53:20
%S A302544 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 A302544 16,27,41,46,30,44,19,33,17,22,36,47,25,39,20,28,21,23,31,45,29,37,48,
%U A302544 50,49,51,56,58,54,59,52,57,53,55,60,62,61,63,74,106,66
%N A302544 Lexicographically earliest sequence of distinct nonnegative numbers such that for any n >= 0, A065359(a(n)) = - A065359(n).
%C A302544 This sequence is a self-inverse permutation of the nonnegative numbers, with fixed points A039004.
%C A302544 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 A302544 This sequence has similarities with A298847.
%C A302544 The scatter plots have an interesting, "fibrous" look. - _Antti Karttunen_, Jul 21 2018
%H A302544 Rémy Sigrist, <a href="/A302544/b302544.txt">Table of n, a(n) for n = 0..16384</a>
%H A302544 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 A302544 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 A302544 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 A302544 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 A302544 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 A302544 Rémy Sigrist, <a href="/A302544/a302544.txt">C++ program for A302544</a>
%H A302544 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A302544 The first terms, alongside the binary representations of n and of a(n), and A065359(n), are:
%e A302544   n   a(n)  bin(n)  bin(a(n))  A065359(n)
%e A302544   --  ----  ------  ---------  ----------
%e A302544    0     0       0       0      0
%e A302544    1     2       1      10      1
%e A302544    2     1      10       1     -1
%e A302544    3     3      11      11      0
%e A302544    4     8     100    1000      1
%e A302544    5    10     101    1010      2
%e A302544    6     6     110     110      0
%e A302544    7    11     111    1011      1
%e A302544    8     4    1000     100     -1
%e A302544    9     9    1001    1001      0
%e A302544   10     5    1010     101     -2
%e A302544   11     7    1011     111     -1
%e A302544   12    12    1100    1100      0
%e A302544   13    14    1101    1110      1
%e A302544   14    13    1110    1101     -1
%e A302544   15    15    1111    1111      0
%e A302544   16    26   10000   11010      1
%e A302544   17    34   10001  100010      2
%e A302544   18    18   10010   10010      0
%e A302544   19    32   10011  100000      1
%e A302544   20    40   10100  101000      2
%o A302544 (C++) See Links section.
%Y A302544 Cf. A039004 (fixed points), A065359, A298847.
%K A302544 nonn,look,base
%O A302544 0,2
%A A302544 _Rémy Sigrist_, Apr 09 2018