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

1,3

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.

Links

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

Formula

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

Example

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 ...

Mathematica

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

Prog

(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

Crossrefs

Cf. A010060, A104248.

Cf. A001285, A010059, A026465.

Sequence in context: A136436 A276729 A257629 * A167677 A278387 A351617

Adjacent sequences: A143328 A143329 A143330 * A143332 A143333 A143334

Keyword

nonn,easy,changed

Author

Ray Chandler, Aug 08 2008

Status

approved