Per Nørgård's Infinity Sequence

The number associated with my diurnal yesterday (27159) has a property that qualifies it for inclusion in OEIS A083866:

A083866

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

This naturally led me find out what the Per Nørgård's infinity sequence was all about. So let's look at OEIS A004718.

A004718

The Danish composer Per Nørgård's "infinity sequence", invented in an attempt to unify in a perfect way repetition and variation: a(2\(n\)) = -a(\(n\)), a(2\(n\)+1) = a(\(n\)) + 1, a(0) = 0.

The first one hundred terms are:

0, 1, -1, 2, 1, 0, -2, 3, -1, 2, 0, 1, 2, -1, -3, 4, 1, 0, -2, 3, 0, 1, -1, 2, -2, 3, 1, 0, 3, -2, -4, 5, -1, 2, 0, 1, 2, -1, -3, 4, 0, 1, -1, 2, 1, 0, -2, 3, 2, -1, -3, 4, -1, 2, 0, 1, -3, 4, 2, -1, 4, -3, -5, 6, 1, 0, -2, 3, 0, 1, -1, 2, -2, 3, 1, 0, 3, -2, -4, 5, 0, 1, -1, 2, 1, 0, -2, 3, -1, 2, 0, 1, 2, -1, -3, 4, -2, 3, 1, 0

The maximum is 6 and the minimum is -5. If we extend the number of terms to 10,000, the maximum is 13 and the minimum is -12. Extending to one million returns a maximum of 19 and a minimum of -18. Figure 1 shows a graph of the first one hundred terms.

Figure 1: permalink

There's an extensive literature out there regarding this sequence and the music associated with it but I won't go into that here. This is post is just to reference the sequence and explain how the terms are generated.