%I #11 Mar 01 2023 02:08:59
%S 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 18,17,16,19,21,22,46,47,48,50,49,54,55,59,60,61,63,62,58,56,57,52,51,
%U 53,39,40,36,35,34,32,33,37,38,42,41,43,44,45,91,92,93,94
%N 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 We ignore leading zeros (and 0 is assumed to have binary length 0).
%C This sequence is a permutation of the nonnegative integers with inverse A360983.
%C 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 Rémy Sigrist, <a href="/A360982/b360982.txt">Table of n, a(n) for n = 0..8191</a>
%H Rémy Sigrist, <a href="/A360982/a360982.png">Scatterplot of the first 2^15 terms</a>
%H Rémy Sigrist, <a href="/A360982/a360982.gp.txt">PARI program</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 length of their first powers, are:
%e n a(n) w1 w2 w3 w4 w5 w6
%e -- ---- -- -- -- -- -- --
%e 0 0 0
%e 1 1 1
%e 2 3 2 4
%e 3 2 2 3
%e 4 6 3 6 8
%e 5 7 3 6 9
%e 6 5 3 5 7 10
%e 7 4 3 5 7 9
%e 8 12 4 8 11
%e 9 15 4 8 12 16 20 24
%e 10 14 4 8 12 16 20 23
%e 11 13 4 8 12 15
%e 12 10 4 7 10 14
%e 13 9 4 7 10 13 16 20
%e 14 8 4 7 10 13 16 19
%e 15 11 4 7 11
%o (PARI) See Links section.
%Y See A360959 for a similar sequence.
%Y Cf. A360963, A360983 (inverse).
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Feb 27 2023