A175930 Concatenation of run lengths in binary expansion of n, written in base 2, then converted to base 10.

1, 3, 2, 6, 7, 5, 3, 7, 13, 15, 14, 10, 11, 7, 4, 12, 15, 27, 26, 30, 31, 29, 15, 11, 21, 23, 22, 14, 15, 9, 5, 13, 25, 31, 30, 54, 55, 53, 27, 31, 61, 63, 62, 58, 59, 31, 28, 20, 23, 43, 42, 46, 47, 45, 23, 15, 29, 31, 30, 18, 19, 11, 6, 14, 27, 51, 50, 62, 63, 61, 31, 55, 109, 111

Offset

1,2

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Formula

From Rémy Sigrist, Jul 02 2019: (Begin)

a(2^k-1) = k for any k > 0.

a(2^k) = A004755(k) for any k > 0.

(End)

Example

6 = 110, two runs, lengths 2 and 1, so we write down 101 and convert it to base 10, getting 5. So a(6) = 5.

Mathematica

f[n_] := FromDigits[Flatten[IntegerDigits[Length /@ Split[IntegerDigits[n, \ 2]], 2]], 2]
Array[f, NUMBER OF TERMS]

Prog

(PARI) a(n) = my (b=[]); while (n, my (x=valuation(n+(n%2), 2)); b = concat(binary(x), b); n \= 2^x); fromdigits(b, 2) \\ Rémy Sigrist, Jul 02 2019
(Python)
from itertools import groupby
def a(n):
    c = "".join(bin(len(list(g)))[2:] for k, g in groupby(bin(n)[2:]))
    return int(c, 2)
print([a(n) for n in range(1, 75)]) # Michael S. Branicky, Oct 02 2021

Crossrefs

Cf. A004755, A101211, A321226.

Sequence in context: A236341 A293835 A258145 * A369272 A265346 A204939

Adjacent sequences: A175927 A175928 A175929 * A175931 A175932 A175933

Keyword

base,easy,look,nonn

Author

Dylan Hamilton, Oct 23 2010

Extensions

Edited by N. J. A. Sloane, Oct 23 2010

Status

approved