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

Author

Reinhard Zumkeller, Jan 02 2012

Keywords

• nonn

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

Crossrefs

Cf. A020985.

Programs

Haskell

import Data.List (group)
a203531 n = a203531_list !! n
a203531_list = map length $ group a020985_list

Mathematica

Map[Length, Most[Split[RudinShapiro[Range[0, 200]]]]] (* Paolo Xausa, Jan 29 2025 *)

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