Pentagonal Number Calculator
Enter n to get P(n) = n(3n-1)/2, check if any integer is pentagonal, or generate a sequence of pentagonal numbers.
Formula: P(n) = n × (3n − 1) / 2
Lists P(1), P(2), …, P(N)
Checks whether the number is pentagonal and returns its index if so.
Formula Reference
General term
P(n) = n(3n−1)/2
First term P(1)
1
Recurrence
P(n) = P(n−1) + 3n−2
Reverse check
(1+√(1+24x))/6 ∈ ℤ⁺
Enter a value and click Calculate
Pentagonal Number
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P(n) = …
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First N Pentagonal Numbers
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Summary
Enter n to get P(n) = n(3n-1)/2, check if any integer is pentagonal, or generate a sequence of pentagonal numbers.
How it works
- Enter a positive integer n to compute the nth pentagonal number.
- The formula P(n) = n(3n-1)/2 is applied instantly in your browser.
- Use the sequence tab to list the first N pentagonal numbers.
- Use the reverse-check tab to test whether any integer is a pentagonal number.
Use cases
- Verify pentagonal numbers for math homework or exams.
- Explore polygonal number sequences for number theory research.
- Generate pentagonal number sequences for programming challenges.
- Check if a given integer belongs to the pentagonal sequence.
- Understand the geometric connection to pentagons in combinatorics.
Frequently Asked Questions
Last updated: 2026-06-13 ·
Reviewed by Nham Vu