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Perrin number

Perrin number is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Perrin number rather than just read about it. In short: In mathematics, the Perrin numbers are a doubly infinite constant-recursive integer sequence with characteristic equation x3 = x + 1. The Perrin numbers, named after the French engineer Raoul Perrin, bear the same relationship to the Padovan sequence as the Lucas numbers do to the Fibonacci sequence.

Perrin number — main illustration
Perrin number — illustration

Key takeaways

  • Perrin number belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Perrin number to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Perrin number from memory before moving on to harder problems.

Reference excerpt

In mathematics, the Perrin numbers are a doubly infinite constant-recursive integer sequence with characteristic equation x3 = x + 1. The Perrin numbers, named after the French engineer Raoul Perrin, bear the same relationship to the Padovan sequence as the Lucas numbers do to the Fibonacci sequence.

Definition The Perrin numbers are defined by the recurrence relation

P ( 0 ) = 3 , P ( 1 ) = 0 , P ( 2 ) = 2 , P ( n ) = P ( n − 2 ) + P ( n − 3 ) for n > 2 , {\displaystyle {\begin{aligned}P(0)&=3,\\P(1)&=0,\\P(2)&=2,\\P(n)&=P(n-2)+P(n-3){\mbox{ for }}n>2,\end{aligned}}}

and the reverse

P ( n ) = P ( n + 3 ) − P ( n + 1 ) for n < 0. {\displaystyle P(n)=P(n+3)-P(n+1){\mbox{ for }}n<0.}

The first few terms in both directions are

Perrin numbers can be expressed as sums of the three initial terms

… excerpt ends here. Continue reading the full article.

Illustrations

Perrin number: Spiral of equilateral triangles with side lengths equal to Perrin numbers.
Spiral of equilateral triangles with side lengths equal to Perrin numbers.
Perrin number: A Perrin microcosm: the escape time algorithm is applied to the Newton map of the entire Perrin function F(z) around critical point z = 1.225432 with viewport width 0.05320. The basins of attraction emanating from the centre correspond to the infinite number of real (left) and complex roots (right) F(z) = 0.
A Perrin microcosm: the escape time algorithm is applied to the Newton map of the entire Perrin function F(z) around critical point z = 1.225432 with viewport width 0.05320. The basins of attraction emanating from the centre correspond to the infinite number of real (left) and complex roots (right) F(z) = 0.
Perrin number: The Perrin function extends the sequence to real numbers.
The Perrin function extends the sequence to real numbers.

Worked examples

Example 1 — a first encounter with Perrin number

Start with the simplest possible case. Write down what Perrin number claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Perrin number before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Perrin number ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Perrin number

In research
Perrin number appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Perrin number in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Perrin number is common in secondary-school and first-year university syllabi. It links to neighbouring topics Integer sequences, Primality tests, Pseudoprimes, so understanding it makes those chapters shorter.
In everyday life
Look for Perrin number outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Perrin number in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Perrin number means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Perrin number out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Perrin number in simple terms?

In mathematics, the Perrin numbers are a doubly infinite constant-recursive integer sequence with characteristic equation x3 = x + 1. The Perrin numbers, named after the French engineer Raoul Perrin, bear the same relationship to the Padovan sequence as the Lucas numbers do to the Fibonacci sequenc…

Why does Perrin number matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Perrin number?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Perrin number.

Tags

  • Integer sequences
  • Primality tests
  • Pseudoprimes
  • Recurrence relations

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