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A360959 Order the nonnegative integers by increasing number of digits in base 2, then by decreasing number of digits in base 3, then by increasing number of digits in base 4, etc.

%I A360959 #17 Mar 01 2023 02:09:21
%S A360959 0,1,3,2,5,7,6,4,9,11,13,15,14,12,10,8,27,29,31,30,28,25,26,17,19,21,
%T A360959 23,24,22,20,18,16,33,35,34,32,49,51,53,55,57,59,61,63,62,60,58,56,54,
%U A360959 52,50,37,39,41,43,45,47,48,46,44,42,40,38,36,125,127,126
%N A360959 Order the nonnegative integers by increasing number of digits in base 2, then by decreasing number of digits in base 3, then by increasing number of digits in base 4, etc.
%C A360959 We ignore leading zeros.
%C A360959 This sequence is a permutation of the nonnegative integers with inverse A360960.
%C A360959 The order of appearance of two distinct integers, say x and y with x > y, depends on the parity of A360964(x, y): even implies x appears after y, odd implies x appears before y.
%H A360959 Rémy Sigrist, <a href="/A360959/b360959.txt">Table of n, a(n) for n = 0..8191</a>
%H A360959 Rémy Sigrist, <a href="/A360959/a360959.gp.txt">PARI program</a>
%H A360959 Rémy Sigrist, <a href="/A360959/a360959.png">Scatterplot of the first 2^15 terms</a>
%H A360959 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A360959 a(n) < 2^k for any n < 2^k.
%e A360959 The first terms, alongside their number of digits in small bases, are:
%e A360959   n   a(n)  w2  w3  w4  w5  w6  w7  w8  w9  w10  w11  w12  w13  w14  w15
%e A360959   --  ----  --  --  --  --  --  --  --  --  ---  ---  ---  ---  ---  ---
%e A360959    0     0   0
%e A360959    1     1   1
%e A360959    2     3   2   2
%e A360959    3     2   2   1
%e A360959    4     5   3   2   2   2   1
%e A360959    5     7   3   2   2   2   2   2
%e A360959    6     6   3   2   2   2   2   1
%e A360959    7     4   3   2   2   1
%e A360959    8     9   4   3   2   2   2   2   2   2    1
%e A360959    9    11   4   3   2   2   2   2   2   2    2    2    1
%e A360959   10    13   4   3   2   2   2   2   2   2    2    2    2    2    1
%e A360959   11    15   4   3   2   2   2   2   2   2    2    2    2    2    2    2
%e A360959   12    14   4   3   2   2   2   2   2   2    2    2    2    2    2    1
%e A360959   13    12   4   3   2   2   2   2   2   2    2    2    2    1
%e A360959   14    10   4   3   2   2   2   2   2   2    2    1
%e A360959   15     8   4   2
%o A360959 (PARI) See Links section.
%Y A360959 See A360982 for a similar sequence.
%Y A360959 Cf. A360960 (inverse), A360964.
%K A360959 nonn,base
%O A360959 0,3
%A A360959 _Rémy Sigrist_, Feb 27 2023