A143331 Lengths of successive runs of 0's in the Thue-Morse sequence A010060.

1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2

Offset: 1

Author

Ray Chandler, Aug 08 2008

Keywords

• nonn
• easy

Comments

Also lengths of successive runs of 1's in the Thue-Morse sequence A010059.

Also lengths of successive runs of 1's in the Thue-Morse sequence A001285.

Examples

			A010060 begins 011010011001011010010110011010011... so the runs of 0's have lengths 1 1 2 2 1 1 2 1 2 1 2 2 1 2 1 2 1 1 ...
		

Links

• Ray Chandler, Table of n, a(n) for n=1..10923

Crossrefs

Cf. A010060, A104248.

Cf. A001285, A010059, A026465.

Programs

Mathematica

Map[Length,Most[Split[ThueMorse[Range[0,500]]]][[;;;;2]]] (* Paolo Xausa, Dec 19 2023 *)

Python

def A143331(n):
    if n==1: return 1
    def iterfun(f,n=0):
        m, k = n, f(n)
        while m != k: m, k = k, f(k)
        return m
    def f(x):
        c, s = x, bin(x)[2:]
        l = len(s)
        for i in range(l&1^1,l,2):
            c -= int(s[i])+int('0'+s[:i],2)
        return c
    return iterfun(lambda x:f(x)+(n<<1)-1,(n<<1)-1)-iterfun(lambda x:f(x)+(n-1<<1),(n-1<<1)) # Chai Wah Wu, Jan 30 2025

Formula

a(n) = A026465(2n-1).