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A203463 Where Golay-Rudin-Shapiro sequence A020985 is positive.

%I A203463 #27 Feb 12 2023 03:09:23
%S A203463 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,
%T A203463 39,40,41,42,46,51,54,56,57,58,62,64,65,66,68,69,71,72,73,74,78,80,81,
%U A203463 82,84,85,87,91,92,93,95,99,102,107,108,109,111,112,113,114
%N A203463 Where Golay-Rudin-Shapiro sequence A020985 is positive.
%C A203463 A020985(a(n)) = 1.
%C A203463 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
%H A203463 Reinhard Zumkeller, <a href="/A203463/b203463.txt">Table of n, a(n) for n = 1..10000</a>
%H A203463 Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016.
%t A203463 GRS = Table[RudinShapiro[n], {n, 0, 200}];
%t A203463 Position[GRS, _?Positive] - 1 // Flatten (* _Jean-François Alcover_, Dec 11 2018 *)
%o A203463 (Haskell)
%o A203463 import Data.List (elemIndices)
%o A203463 a203463 n = a203463_list !! (n-1)
%o A203463 a203463_list = elemIndices 1 a020985_list
%o A203463 (Python)
%o A203463 from itertools import count, islice
%o A203463 def A203463_gen(startvalue=0): # generator of terms >= startvalue
%o A203463     return filter(lambda n:(n&(n>>1)).bit_count()&1^1,count(max(startvalue,0)))
%o A203463 A203463_list = list(islice(A203463_gen(),30)) # _Chai Wah Wu_, Feb 11 2023
%Y A203463 Cf. A022155 (complement), A020985.
%K A203463 nonn
%O A203463 1,3
%A A203463 _Reinhard Zumkeller_, Jan 02 2012