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

0, 5, 10, 17, 20, 27, 34, 40, 45, 54, 65, 68, 75, 80, 85, 90, 99, 105, 108, 119, 130, 136, 141, 150, 160, 165, 170, 177, 180, 187, 198, 210, 216, 221, 238, 257, 260, 267, 272, 277, 282, 291, 297, 300, 311, 320, 325, 330, 337, 340, 347, 354, 360

Offset: 0

Author

Ralf Stephan, May 07 2003

Keywords

• nonn

Comments

First differences seem to be always >2.

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

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Yu Hin (Gary) Au, Christopher Drexler-Lemire, and Jeffrey Shallit, Notes and note pairs in Norgard's infinity series, Journal of Mathematics and Music, Volume 11, Issue 1, 2017, pages 1-19.

Crossrefs

Cf. A004718, A005107.

Programs

Haskell

a083866 n = a083866_list !! n
a083866_list = filter ((== 0) . a004718) [0..]
-- Reinhard Zumkeller, Mar 19 2015, Nov 10 2012

Python

from itertools import groupby, islice
def A083866_gen(startvalue=0): # generator of terms >= startvalue
    n, c = max(0,startvalue),0
    for k, g in groupby(bin(n)[2:]):
        c = c+len(list(g)) if k == '1' else (-c if len(list(g))&1 else c)
    while True:
        if c == 0: yield n
        n += 1
        c = c-t-1 if (t:=(~n & n-1).bit_length())&1 else t+1-c
A083866_list = list(islice(A083866_gen(),20)) # Chai Wah Wu, Mar 02 2023