gives the n term in the Rudin–Shapiro sequence.
- RudinShapiro[n] is 1 if n has an even number of possibly overlapping 11 sequences in its base-2 digits, and is -1 otherwise.
- RudinShapiro automatically threads over lists.
Examplesopen allclose all
Basic Examples (2)
The sixth element of the Rudin–Shapiro sequence:
The number 6 has an odd number of 11 sequences in its binary form:
The first ten elements of the sequence:
Display the values alongside the binary expansion:
RudinShapiro threads over lists:
Evaluate at large integers:
Generate an example of a first Shapiro polynomial:
Generate a Rudin–Shapiro curve:
Properties & Relations (3)
The Rudin–Shapiro sequence has a nested structure:
The Rudin–Shapiro sequence satisfies a recurrence relation:
The Rudin–Shapiro sequence is the result of a substitution system:
Neat Examples (1)
Generate a path based on the Rudin–Shapiro sequence:
Introduced in 2015