A203463 Where Golay-Rudin-Shapiro sequence A020985 is positive.

0, 1, 2, 4, 5, 7, 8, 9, 10, 14, 16, 17, 18, 20, 21, 23, 27, 28, 29, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 46, 51, 54, 56, 57, 58, 62, 64, 65, 66, 68, 69, 71, 72, 73, 74, 78, 80, 81, 82, 84, 85, 87, 91, 92, 93, 95, 99, 102, 107, 108, 109, 111, 112, 113, 114

Offset

1,3

Comments

A020985(a(n)) = 1.

Or numbers n for which numbers of 1's and runs of 1's in binary representation have the same parity: A010060(n)=A268411(n). - Vladimir Shevelev, Feb 10 2016

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Mathematica

GRS = Table[RudinShapiro[n], {n, 0, 200}];
Position[GRS, _?Positive] - 1 // Flatten (* Jean-François Alcover, Dec 11 2018 *)

Prog

(Haskell)
import Data.List (elemIndices)
a203463 n = a203463_list !! (n-1)
a203463_list = elemIndices 1 a020985_list
(Python)
from itertools import count, islice
def A203463_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:(n&(n>>1)).bit_count()&1^1, count(max(startvalue, 0)))
A203463_list = list(islice(A203463_gen(), 30)) # Chai Wah Wu, Feb 11 2023

Crossrefs

Cf. A022155 (complement), A020985.

Sequence in context: A039069 A285423 A173025 * A223909 A010392 A095042

Adjacent sequences: A203460 A203461 A203462 * A203464 A203465 A203466

Keyword

nonn

Author

Reinhard Zumkeller, Jan 02 2012

Status

approved