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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A203463 (complement), A020985.

Sequence in context: A028744 A028775 A223910 * A066157 A073159 A000419

Adjacent sequences: A022152 A022153 A022154 * A022156 A022157 A022158

Keyword

nonn

Author

Robert G. Wilson v

Status

approved