A043556 Number of runs in base-4 representation of n.

1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 3, 3, 3, 2, 1, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 2, 2, 1, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 2, 1, 2, 3, 3, 3, 4, 3, 4, 4, 4, 4, 3, 4, 4, 4, 4, 3, 2, 3, 3, 3, 2, 1, 2, 2, 3, 3

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Every positive integers occurs infinitely many times. See A297770 for a guide to related sequences.

Crossrefs

Cf. A297772 (number of distinct runs), A297770.

Programs

Mathematica

b = 4; s[n_] := Length[Split[IntegerDigits[n, b]]];
Table[s[n], {n, 1, 200}]

Python

from itertools import groupby
from sympy.ntheory import digits
def A043556(n): return len(list(groupby(digits(n,4)[1:]))) # Chai Wah Wu, Jul 13 2024

Formula

a(n) << log n. In particular, a(n) <= log(n)/log(4) + 1. - Charles R Greathouse IV, Jul 13 2024

Extensions

Updated by Clark Kimberling, Feb 03 2018