A318926 Take the binary expansion of n, starting with the least significant bit, and concatenate the lengths of the runs.

1, 11, 2, 21, 111, 12, 3, 31, 121, 1111, 211, 22, 112, 13, 4, 41, 131, 1121, 221, 2111, 11111, 1211, 311, 32, 122, 1112, 212, 23, 113, 14, 5, 51, 141, 1131, 231, 2121, 11121, 1221, 321, 3111

Offset

1,2

Comments

Obviously this compressed notation is useful only for n < 1023. A227736 is a version which works for all n.

Links

Table of n, a(n) for n=1..40.

Claude Lenormand, Deux transformations sur les mots, Preprint, 5 pages, Nov 17 2003. Apparently unpublished. This is a scanned copy of the version that the author sent to me in 2003. - N. J. A. Sloane, Sep 09 2018. See Procedure 1.

Example

n, binary, run lengths, -> a(n)
1, [1], [1] -> 1
2, [0, 1], [1, 1] -> 11
3, [1, 1], [2] ->  2
4, [0, 0, 1], [2, 1] -> 21
5, [1, 0, 1], [1, 1, 1] -> 111
6, [0, 1, 1], [1, 2] -> 12
7, [1, 1, 1], [3] -> 3
8, [0, 0, 0, 1], [3, 1] ->  31,
...

Prog

(Python)
from itertools import groupby
def A318926(n): return int(''.join(str(len(list(g))) for k, g in groupby(bin(n)[:1:-1]))) # Chai Wah Wu, Mar 11 2022

Crossrefs

Cf. A227736, A101211, A318927.

Sequence in context: A262369 A092260 A370004 * A336874 A040120 A365220

Adjacent sequences: A318923 A318924 A318925 * A318927 A318928 A318929

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 09 2018

Status

approved