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Single-digit numbers in the order in which they first appear in the decimal expansions of powers of 2, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.
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%I #34 Jan 23 2019 08:37:31

%S 1,2,4,8,6,3,5,0,9,7,16,32,64,12,28,25,56,51,10,24,20,48,40,96,81,19,

%T 92,63,38,84,27,76,68,65,55,53,36,13,31,72,26,62,21,14,44,52,42,88,85,

%U 57,97,71,15,41,94,43,30,83,86,60,67,77,33,35,54,34,17,45

%N Single-digit numbers in the order in which they first appear in the decimal expansions of powers of 2, followed by the two-digit numbers in the order in which they appear, then the three-digit numbers, and so on.

%C Apparently this algorithm applied to most sequences will produce a fractal scatterplot graph. - _David Williams_, Jan 20 2019

%H Rémy Sigrist, <a href="/A321043/b321043.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A321043/a321043.gp.txt">PARI program for A321043</a>

%e 1,2,4,8,16,32,64,128,256,512,1024, ..., 4096, ..., 32768, ... gives 1,2,4,8,6,3,5,0,9,7.

%e Then we get 16,32,64,12,28,25,56,51,10,24,20,48,40,96,81,19,92,...

%e 11 does not appear until 2^40 = 1099511627776.

%o (PARI) See Links section.

%Y Cf. A000079, A105177.

%Y See A030000 for an inverse.

%K nonn,base,look

%O 1,2

%A _David Williams_, Oct 26 2018

%E Edited by _N. J. A. Sloane_, Oct 27 2018

%E More terms from _Rémy Sigrist_, Oct 27 2018