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

1,2

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.

Example

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

Prog

(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

Crossrefs

See A095684 for a better version. Different from A110382.

Sequence in context: A278985 A071159 A231873 * A110382 A095764 A342944

Adjacent sequences: A096296 A096297 A096298 * A096300 A096301 A096302

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 25 2004

Extensions

More terms from John W. Layman, Oct 07 2004

Status

approved