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A022155
Values of n at which Golay-Rudin-Shapiro sequence A020985 is negative.
4
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
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
KEYWORD
nonn
STATUS
approved

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