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A083866 Positions of zeros in Per Nørgård's infinity sequence (A004718).

%I A083866 #27 Jul 08 2023 08:05:47
%S A083866 0,5,10,17,20,27,34,40,45,54,65,68,75,80,85,90,99,105,108,119,130,136,
%T A083866 141,150,160,165,170,177,180,187,198,210,216,221,238,257,260,267,272,
%U A083866 277,282,291,297,300,311,320,325,330,337,340,347,354,360
%N A083866 Positions of zeros in Per Nørgård's infinity sequence (A004718).
%C A083866 First differences seem to be always >2.
%C A083866 Many (but not all) prime members are in A005107.
%C A083866 The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.
%H A083866 Reinhard Zumkeller, <a href="/A083866/b083866.txt">Table of n, a(n) for n = 0..10000</a>
%H A083866 Yu Hin (Gary) Au, Christopher Drexler-Lemire, and Jeffrey Shallit, <a href="https://doi.org/10.1080/17459737.2017.1299807">Notes and note pairs in Norgard's infinity series</a>, Journal of Mathematics and Music, Volume 11, Issue 1, 2017, pages 1-19.
%o A083866 (Haskell)
%o A083866 a083866 n = a083866_list !! n
%o A083866 a083866_list = filter ((== 0) . a004718) [0..]
%o A083866 -- _Reinhard Zumkeller_, Mar 19 2015, Nov 10 2012
%o A083866 (Python)
%o A083866 from itertools import groupby, islice
%o A083866 def A083866_gen(startvalue=0): # generator of terms >= startvalue
%o A083866     n, c = max(0,startvalue),0
%o A083866     for k, g in groupby(bin(n)[2:]):
%o A083866         c = c+len(list(g)) if k == '1' else (-c if len(list(g))&1 else c)
%o A083866     while True:
%o A083866         if c == 0: yield n
%o A083866         n += 1
%o A083866         c = c-t-1 if (t:=(~n & n-1).bit_length())&1 else t+1-c
%o A083866 A083866_list = list(islice(A083866_gen(),20)) # _Chai Wah Wu_, Mar 02 2023
%Y A083866 Cf. A004718, A005107.
%K A083866 nonn
%O A083866 0,2
%A A083866 _Ralf Stephan_, May 07 2003