A022155 Values of n at which Golay-Rudin-Shapiro sequence A020985 is negative.

3, 6, 11, 12, 13, 15, 19, 22, 24, 25, 26, 30, 35, 38, 43, 44, 45, 47, 48, 49, 50, 52, 53, 55, 59, 60, 61, 63, 67, 70, 75, 76, 77, 79, 83, 86, 88, 89, 90, 94, 96, 97, 98, 100, 101, 103, 104, 105, 106, 110, 115, 118, 120, 121, 122, 126, 131, 134, 139, 140

Offset: 1

Author

Robert G. Wilson v

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 distinct parities: A010060(n) = 1 - A268411(n). - Vladimir Shevelev, Feb 10 2016

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• J. Brillhart and P. Morton, A case study in mathematical research: the Golay-Rudin-Shapiro sequence, Amer. Math. Monthly, 103 (1996) 854-869.
• Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Crossrefs

Cf. A203463 (complement), A020985.

Programs

Haskell

import Data.List (elemIndices)
a022155 n = a022155_list !! (n-1)
a022155_list = elemIndices (- 1) a020985_list
-- Reinhard Zumkeller, Jan 02 2012

Mathematica

Position[Array[RudinShapiro, 200, 0], ?Negative] - 1 // Flatten (* _Jean-François Alcover, Dec 04 2018 *)

Python

from itertools import count, islice
def A022155_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:(n&(n>>1)).bit_count()&1,count(max(startvalue,0)))
A022155_list = list(islice(A022155_gen(),30)) # Chai Wah Wu, Feb 11 2023