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RudinShapiro[n]

gives the n^(th) term in the Rudin–Shapiro sequence.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Neat Examples  
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RudinShapiro

RudinShapiro[n]

gives the n^(th) term in the Rudin–Shapiro sequence.

Details

  • 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.

Examples

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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:

Scope  (2)

RudinShapiro threads over lists:

Evaluate at large integers:

Applications  (2)

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:

Wolfram Research (2015), RudinShapiro, Wolfram Language function, https://reference.wolfram.com/language/ref/RudinShapiro.html.

Text

Wolfram Research (2015), RudinShapiro, Wolfram Language function, https://reference.wolfram.com/language/ref/RudinShapiro.html.

CMS

Wolfram Language. 2015. "RudinShapiro." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RudinShapiro.html.

APA

Wolfram Language. (2015). RudinShapiro. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RudinShapiro.html

BibTeX

@misc{reference.wolfram_2025_rudinshapiro, author="Wolfram Research", title="{RudinShapiro}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/RudinShapiro.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_rudinshapiro, organization={Wolfram Research}, title={RudinShapiro}, year={2015}, url={https://reference.wolfram.com/language/ref/RudinShapiro.html}, note=[Accessed: 13-August-2025]}