Pentagonal Number Checker
Check whether a nonnegative safe integer equals k(3k-1)/2 for some integer k >= 1.
Description
Check whether a nonnegative safe integer equals k(3k-1)/2 for some integer k >= 1.
Check whether a nonnegative safe integer equals k(3k-1)/2 for some integer k >= 1.
When to use Pentagonal Number Checker
Use this tool to test or transform exact integers according to the named number-theory definition, for education, validation, or algorithm checks.
- Integer
- An integer input greater than or equal to 0.
How the calculation works
The formula below determines the tool output. Is a pentagonal number: Whether is a pentagonal number is true.1
Pₖ = k(3k − 1) / 2 Limitations and assumptions
This tool applies an exact integer definition within JavaScript's safe-integer range. It is not an arbitrary-precision factorization or proof system, so do not use rounded measurements or integers beyond the accepted domain as though they were exact.
Alternative or Complementary approaches
Complement a number-property result with its factorization, divisors, digit representation, or a second independent predicate. A true result establishes only the named property and does not imply other properties such as primality.
References
-
Pentagonal number — Wikipedia contributors
Similar or alternative tools
- Catalan Number Checker
Check whether a nonnegative safe integer is a Catalan number generated with the exact recurrence C(k+1) = C(k) * 2(2k+1) / (k+2).
- Fibonacci Number Checker
Check whether a nonnegative safe integer is a Fibonacci number.
- Lucas Number Checker
Check whether a nonnegative safe integer equals a Lucas number L(0)=2, L(1)=1, ...