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

0,5

Comments

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

Links

Table of n, a(n) for n=0..89.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A270746 A043531 A297772 * A230643 A344117 A163367

Adjacent sequences: A043553 A043554 A043555 * A043557 A043558 A043559

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Updated by Clark Kimberling, Feb 03 2018

Status

approved