A104248 Lengths of successive runs of 1's in the Thue-Morse sequence A010060.

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

Offset: 1

Author

N. J. A. Sloane, Aug 05 2008

Keywords

• nonn
• easy

Comments

Also lengths of successive runs of 0's in the Thue-Morse sequence A010059.

Also lengths of successive runs of 2's in the Thue-Morse sequence A001285.

A variant of A036577, suggested by p. 4421 of Grytczuk.

Examples

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

Links

• Ray Chandler, Table of n, a(n) for n=1..10922
• Jaroslaw Grytczuk, Thue type problems for graphs, points and numbers, Discrete Math., 308 (2008), 4419-4429.

Crossrefs

Cf. A010060, A036577, A143331.

Cf. A001285, A010059, A026465.

Programs

Mathematica

Map[Length,Most[Split[ThueMorse[Range[500]]]][[;;;;2]]] (* Paolo Xausa, Dec 19 2023 *)
Length/@DeleteCases[Split[ThueMorse[Range[450]]],?(#[[1]]==0&)] (* _Harvey P. Dale, Nov 09 2024 *)

Python

def A104248(n):
    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),n<<1)-iterfun(lambda x:f(x)+(n<<1)-1,(n<<1)-1) # Chai Wah Wu, Jan 30 2025

Formula

a(n) = A026465(2n).

Extensions

Edited and extended by Ray Chandler, Aug 08 2008