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

0,3

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A020985, A020986.

Sequence in context: A128432 A195198 A039966 * A089451 A145099 A374045

Adjacent sequences: A380664 A380665 A380666 * A380668 A380669 A380670

Keyword

sign,easy

Author

Paolo Xausa, Jan 30 2025

Status

approved