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a(1) = 1; for n > 1, let s denote the binary representation of a(n-1) with the first bit omitted. Then a(n) is the smallest number not yet present whose binary representation starts with s, omitting leading zeros.
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%I #19 Sep 20 2015 20:33:55

%S 1,2,3,4,5,6,8,7,12,9,10,11,13,20,16,14,24,17,15,28,25,18,19,26,21,22,

%T 27,23,29,52,40,32,30,56,48,33,31,60,57,50,36,34,35,49,68,37,41,38,51,

%U 39,58,53,42,43,44,96,64,45,54,88,97,66,46,59,55,47,61

%N a(1) = 1; for n > 1, let s denote the binary representation of a(n-1) with the first bit omitted. Then a(n) is the smallest number not yet present whose binary representation starts with s, omitting leading zeros.

%C It seems clear that every number will appear. It would be nice to have a formal proof. - _N. J. A. Sloane_, Sep 20 2015

%H Alois P. Heinz, <a href="/A262374/b262374.txt">Table of n, a(n) for n = 1..20000</a>

%e : 1 ... 1

%e : 10 ... 2

%e : 11 ... 3

%e : 100 ... 4

%e : 101 ... 5

%e : 110 ... 6

%e : 1000 ... 8

%e : 111 ... 7

%e : 1100 ... 12

%e : 1001 ... 9

%e : 1010 ... 10

%e : 1011 ... 11

%e : 1101 ... 13

%e : 10100 ... 20

%e : 10000 ... 16

%e : 1110 ... 14

%e : 11000 ... 24

%e : 10001 ... 17

%Y Binary counterpart of A262356.

%Y A262381 gives the binary representations.

%Y Cf. A262388.

%K nonn,base

%O 1,2

%A _Allan C. Wechsler_, Sep 20 2015