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

Author

Reinhard Zumkeller, Jan 02 2012

Keywords

• nonn

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.

Crossrefs

Cf. A022155 (complement), A020985.

Programs

Haskell

import Data.List (elemIndices)
a203463 n = a203463_list !! (n-1)
a203463_list = elemIndices 1 a020985_list

Mathematica

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

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