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.

1, 11, 12, 111, 112, 122, 123, 1111, 1112, 1122, 1123, 1222, 1223, 1233, 1234, 11111, 11112, 11122, 11123, 11222, 11223, 11233, 11234, 12222, 12223, 12233, 12234, 12333, 12334, 12344, 12345, 111111, 111112, 111122, 111123, 111222, 111223

Offset: 1

Author

N. J. A. Sloane, Jun 25 2004

Keywords

• nonn
• easy

Examples

			The 8 strings of length 4 are 1111, 1112, 1122, 1123, 1222, 1223, 1233, 1234.
		

Links

• Mikhail Kurkov, Table of n, a(n) for n = 1..8191 (n = 1..37 from John W. Layman)
• J. C. Kieffer, W. Szpankowski and E.-H. Yang, Problems on sequences: information theory and computer science interface, IEEE Trans. Inform. Theory, 50 (No. 7, 2004), 1385-1392.

Crossrefs

See A095684 for a better version. Different from A110382.

Programs

PARI

f(n, k) = sum(j=0, k-1, 1 + log(hammingweight(n\(2^j)))\log(10));
a(n) = sum(k=0, log(n)\log(2), hammingweight(n\(2^k))*10^f(n,k)); \\ Michel Marcus, May 09 2019

Extensions

More terms from John W. Layman, Oct 07 2004