Pronic (oblong) number: n(n+1). First: 0,2,6,12,20,30,42,56,72,90,110... Always even. Always twice a triangular number: n(n+1) = 2·T(n). Between consecutive perfect squares: n² < n(n+1) < (n+1)². All pronic numbers are even.
How to Use
Enter number:
- Pronic?: Is it n(n+1)?
- Factors: The consecutive pair
- Triangular: = 2·T(n)
Properties
- Always even (n or n+1 is even)
- Sum of first n even numbers: 2+4+...+2n = n(n+1)
- Never a perfect square
- n(n+1) mod 10 ∈ {0,2,6} only
Geometric Meaning
'Oblong' or 'heteromecic': arranges as an n × (n+1) rectangle. This is why they're called 'rectangular numbers'. They represent the area of a nearly-square rectangle.
Step-by-Step Instructions
- 1Enter number.
- 2Check pronic.
- 3Find factor pair.
- 4Link to triangular.
- 5Browse sequence.