A380667 First differences of the Golay-Rudin-Shapiro sequence (A020985), divided by 2.

0, 0, -1, 1, 0, -1, 1, 0, 0, 0, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, 0, 1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, -1, 1, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, 0, -1, 1, 0, 0, 0, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, 0

Offset: 0

Author

Paolo Xausa, Jan 30 2025

Keywords

• sign
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A020985, A020986.

Programs

Mathematica

Differences[RudinShapiro[Range[0, 100]]]/2

Python

def A380667(n): return (1 if m else -1) if (m:=(n&(n>>1)).bit_count()&1)^((n+1&(n+1>>1)).bit_count()&1) else 0  # Chai Wah Wu, Jan 30 2025

Formula

a(n) = (A020985(n+1) - A020985(n))/2.