Calculators
Perrin Number Calculator
Calculate exact Perrin numbers for indices 0 to 1000 privately in your browser, with the next term and digit count.
Calculate exact terms in the Perrin sequence.
Perrin numbers use P(0) = 3, P(1) = 0 and P(2) = 2. Each later term adds the terms two and three positions earlier: P(n) = P(n − 2) + P(n − 3), for n ≥ 3. The sequence begins 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17. For example, P(10) = P(8) + P(7) = 10 + 7 = 17. The Padovan sequence uses the same recurrence with different starting values, so its results differ. Enter an index from 0 to 1000 using one to four digits; leading zeros and surrounding whitespace are accepted. Signs, decimals, separators and scientific notation are rejected. Exact BigInt addition preserves every digit. Results include the selected term, its decimal digit count and the next term. Zero counts as one digit. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Which starting values does this calculator use?
P(0) = 3, P(1) = 0 and P(2) = 2. The next terms are 3, 2, 5, 5 and 7. Index zero returns 3, and index one returns 0.
How are Perrin numbers calculated?
For n ≥ 3, P(n) = P(n − 2) + P(n − 3). For example, P(10) = 10 + 7 = 17. Padovan numbers use the same recurrence but start with 1, 1, 1 instead of 3, 0, 2.
Are large results exact?
Yes. BigInt addition preserves every digit without rounding. Results include the selected term, the next term and the decimal digit count. Zero counts as one digit.
Which inputs are supported?
Enter an index from 0 to 1000 using one to four digits. Leading zeros and surrounding whitespace are accepted; signs, decimals, separators and scientific notation are rejected. Your inputs stay in your browser.