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

%I A022155 #31 Feb 12 2023 03:08:25
%S A022155 3,6,11,12,13,15,19,22,24,25,26,30,35,38,43,44,45,47,48,49,50,52,53,
%T A022155 55,59,60,61,63,67,70,75,76,77,79,83,86,88,89,90,94,96,97,98,100,101,
%U A022155 103,104,105,106,110,115,118,120,121,122,126,131,134,139,140
%N A022155 Values of n at which Golay-Rudin-Shapiro sequence A020985 is negative.
%C A022155 A020985(a(n)) = -1.
%C A022155 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
%H A022155 Reinhard Zumkeller, <a href="/A022155/b022155.txt">Table of n, a(n) for n = 1..10000</a>
%H A022155 J. Brillhart and P. Morton, <a href="http://www.maa.org/programs/maa-awards/writing-awards/a-case-study-in-mathematical-research-the-golay-rudin-shapiro-sequence">A case study in mathematical research: the Golay-Rudin-Shapiro sequence</a>, Amer. Math. Monthly, 103 (1996) 854-869.
%H A022155 Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016.
%t A022155 Position[Array[RudinShapiro, 200, 0], _?Negative] - 1 // Flatten (* _Jean-François Alcover_, Dec 04 2018 *)
%o A022155 (Haskell)
%o A022155 import Data.List (elemIndices)
%o A022155 a022155 n = a022155_list !! (n-1)
%o A022155 a022155_list = elemIndices (- 1) a020985_list
%o A022155 -- _Reinhard Zumkeller_, Jan 02 2012
%o A022155 (Python)
%o A022155 from itertools import count, islice
%o A022155 def A022155_gen(startvalue=0): # generator of terms >= startvalue
%o A022155     return filter(lambda n:(n&(n>>1)).bit_count()&1,count(max(startvalue,0)))
%o A022155 A022155_list = list(islice(A022155_gen(),30)) # _Chai Wah Wu_, Feb 11 2023
%Y A022155 Cf. A203463 (complement), A020985.
%K A022155 nonn
%O A022155 1,1
%A A022155 _Robert G. Wilson v_