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A360982 Order the nonnegative integers by increasing binary length of values, then by decreasing binary length of values squared, then by increasing binary length of values cubed, etc.

%I A360982 #11 Mar 01 2023 02:08:59
%S A360982 0,1,3,2,6,7,5,4,12,15,14,13,10,9,8,11,23,24,25,27,30,31,29,28,26,20,
%T A360982 18,17,16,19,21,22,46,47,48,50,49,54,55,59,60,61,63,62,58,56,57,52,51,
%U A360982 53,39,40,36,35,34,32,33,37,38,42,41,43,44,45,91,92,93,94
%N A360982 Order the nonnegative integers by increasing binary length of values, then by decreasing binary length of values squared, then by increasing binary length of values cubed, etc.
%C A360982 We ignore leading zeros (and 0 is assumed to have binary length 0).
%C A360982 This sequence is a permutation of the nonnegative integers with inverse A360983.
%C A360982 The order of appearance of two distinct integers, say x and y with x > y, depends on the parity of A360963(x, y): even implies x appears before y, odd implies x appears after y.
%H A360982 Rémy Sigrist, <a href="/A360982/b360982.txt">Table of n, a(n) for n = 0..8191</a>
%H A360982 Rémy Sigrist, <a href="/A360982/a360982.png">Scatterplot of the first 2^15 terms</a>
%H A360982 Rémy Sigrist, <a href="/A360982/a360982.gp.txt">PARI program</a>
%H A360982 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A360982 The first terms, alongside the binary length of their first powers, are:
%e A360982   n   a(n)  w1  w2  w3  w4  w5  w6
%e A360982   --  ----  --  --  --  --  --  --
%e A360982    0     0   0
%e A360982    1     1   1
%e A360982    2     3   2   4
%e A360982    3     2   2   3
%e A360982    4     6   3   6   8
%e A360982    5     7   3   6   9
%e A360982    6     5   3   5   7  10
%e A360982    7     4   3   5   7   9
%e A360982    8    12   4   8  11
%e A360982    9    15   4   8  12  16  20  24
%e A360982   10    14   4   8  12  16  20  23
%e A360982   11    13   4   8  12  15
%e A360982   12    10   4   7  10  14
%e A360982   13     9   4   7  10  13  16  20
%e A360982   14     8   4   7  10  13  16  19
%e A360982   15    11   4   7  11
%o A360982 (PARI) See Links section.
%Y A360982 See A360959 for a similar sequence.
%Y A360982 Cf. A360963, A360983 (inverse).
%K A360982 nonn,base
%O A360982 0,3
%A A360982 _Rémy Sigrist_, Feb 27 2023