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

1,1

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.

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.

Formula

a(n) = A026465(2n).

Example

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 ...

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 *)

Prog

(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

Crossrefs

Cf. A010060, A036577, A143331.

Cf. A001285, A010059, A026465.

Sequence in context: A022934 A107450 A341765 * A358359 A249973 A343854

Adjacent sequences: A104245 A104246 A104247 * A104249 A104250 A104251

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Aug 05 2008

Extensions

Edited and extended by Ray Chandler, Aug 08 2008

Status

approved