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