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%I #11 Jul 02 2020 02:03:29
%S 0,1,2,3,5,6,4,7,10,13,9,14,11,12,8,15,21,26,18,29,22,25,17,30,20,27,
%T 19,28,23,24,16,31,42,53,37,58,45,50,34,61,41,54,38,57,46,49,33,62,43,
%U 52,36,59,44,51,35,60,40,55,39,56,47,48,32,63,85,106,74
%N Nonnegative integers ordered by binary length and then lexicographically by run lengths (considering least significant runs first).
%C The variant where we consider most significant runs first apparently corresponds to A180200.
%H Rémy Sigrist, <a href="/A335858/b335858.txt">Table of n, a(n) for n = 0..8192</a>
%H Rémy Sigrist, <a href="/A335858/a335858.gp.txt">PARI program for A335858</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F Apparently a(n) = A056539(A180200(n)).
%e The first terms, alongside the corresponding binary representation and run lengths, are:
%e n a(n) bin(a(n)) A227736(n, *)
%e -- ---- --------- -------------
%e 0 0 0 ()
%e 1 1 1 (1)
%e 2 2 10 (1, 1)
%e 3 3 11 (2)
%e 4 5 101 (1, 1, 1)
%e 5 6 110 (1, 2)
%e 6 4 100 (2, 1)
%e 7 7 111 (3)
%e 8 10 1010 (1, 1, 1, 1)
%e 9 13 1101 (1, 1, 2)
%e 10 9 1001 (1, 2, 1)
%e 11 14 1110 (1, 3)
%e 12 11 1011 (2, 1, 1)
%e 13 12 1100 (2, 2)
%e 14 8 1000 (3, 1)
%e 15 15 1111 (4)
%o (PARI) See Links section.
%Y Cf. A005811, A180200, A227736.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Jun 27 2020
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