A083866 - OEIS

%I #27 Jul 08 2023 08:05:47

%S 0,5,10,17,20,27,34,40,45,54,65,68,75,80,85,90,99,105,108,119,130,136,

%T 141,150,160,165,170,177,180,187,198,210,216,221,238,257,260,267,272,

%U 277,282,291,297,300,311,320,325,330,337,340,347,354,360

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

%C First differences seem to be always >2.

%C Many (but not all) prime members are in A005107.

%C The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.

%H Reinhard Zumkeller, <a href="/A083866/b083866.txt">Table of n, a(n) for n = 0..10000</a>

%H 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 (Haskell)

%o a083866 n = a083866_list !! n

%o a083866_list = filter ((== 0) . a004718) [0..]

%o -- _Reinhard Zumkeller_, Mar 19 2015, Nov 10 2012

%o (Python)

%o from itertools import groupby, islice

%o def A083866_gen(startvalue=0): # generator of terms >= startvalue

%o     n, c = max(0,startvalue),0

%o     for k, g in groupby(bin(n)[2:]):

%o         c = c+len(list(g)) if k == '1' else (-c if len(list(g))&1 else c)

%o     while True:

%o         if c == 0: yield n

%o         n += 1

%o         c = c-t-1 if (t:=(~n & n-1).bit_length())&1 else t+1-c

%o A083866_list = list(islice(A083866_gen(),20)) # _Chai Wah Wu_, Mar 02 2023

%Y Cf. A004718, A005107.

%K nonn

%O 0,2

%A _Ralf Stephan_, May 07 2003