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A096299 List of strings in lexicographic order with property that for the 2^(m-1) strings of length m, the first entry is 1, the second distinct entry (reading from left to right) is 2, the third distinct entry is 3, etc.

%I A096299 #47 Apr 27 2024 03:34:32
%S A096299 1,11,12,111,112,122,123,1111,1112,1122,1123,1222,1223,1233,1234,
%T A096299 11111,11112,11122,11123,11222,11223,11233,11234,12222,12223,12233,
%U A096299 12234,12333,12334,12344,12345,111111,111112,111122,111123,111222,111223
%N A096299 List of strings in lexicographic order with property that for the 2^(m-1) strings of length m, the first entry is 1, the second distinct entry (reading from left to right) is 2, the third distinct entry is 3, etc.
%H A096299 Mikhail Kurkov, <a href="/A096299/b096299.txt">Table of n, a(n) for n = 1..8191</a> (n = 1..37 from John W. Layman)
%H A096299 J. C. Kieffer, W. Szpankowski and E.-H. Yang, <a href="https://doi.org/10.1109/TIT.2004.830747">Problems on sequences: information theory and computer science interface</a>, IEEE Trans. Inform. Theory, 50 (No. 7, 2004), 1385-1392.
%e A096299 The 8 strings of length 4 are 1111, 1112, 1122, 1123, 1222, 1223, 1233, 1234.
%o A096299 (PARI) f(n, k) = sum(j=0, k-1, 1 + log(hammingweight(n\(2^j)))\log(10));
%o A096299 a(n) = sum(k=0, log(n)\log(2), hammingweight(n\(2^k))*10^f(n,k)); \\ _Michel Marcus_, May 09 2019
%Y A096299 See A095684 for a better version. Different from A110382.
%K A096299 nonn,easy
%O A096299 1,2
%A A096299 _N. J. A. Sloane_, Jun 25 2004
%E A096299 More terms from _John W. Layman_, Oct 07 2004