A203531 Run lengths in Golay-Rudin-Shapiro sequence A020985.

3, 1, 2, 1, 4, 3, 1, 1, 3, 1, 2, 1, 1, 3, 3, 1, 4, 1, 2, 1, 4, 3, 1, 4, 1, 2, 1, 1, 3, 3, 1, 1, 3, 1, 2, 1, 4, 3, 1, 1, 3, 1, 2, 1, 1, 3, 3, 1, 1, 3, 1, 2, 1, 4, 3, 1, 4, 1, 2, 1, 1, 3, 3, 1, 4, 1, 2, 1, 4, 3, 1, 1, 3, 1, 2, 1, 1, 3, 3, 1, 4, 1, 2, 1, 4, 3

Offset

0,1

Comments

a(2*n) = length of n-th run of 1s; a(2*n+1) = length of n-th run of -1s.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Rudin-Shapiro Sequence

Prog

(Haskell)
import Data.List (group)
a203531 n = a203531_list !! n
a203531_list = map length $ group a020985_list
(Python)
from itertools import count, islice
def A203531_gen(): # generator of terms
    c, a = 0, 1
    for n in count(0):
        if (n&(n>>1)).bit_count()&1^a:
            c += 1
        else:
            yield c
            c = 1
            a ^= 1
A293531_list = list(islice(A203531_gen(), 30)) # Chai Wah Wu, Feb 11 2023

Crossrefs

Cf. A020985.

Sequence in context: A257915 A257904 A257980 * A324885 A046645 A284639

Adjacent sequences: A203528 A203529 A203530 * A203532 A203533 A203534

Keyword

nonn

Author

Reinhard Zumkeller, Jan 02 2012

Status

approved