Talk:Pronic number

n squared plus n
How about


 * {| style="text-align: center"

Hyacinth (talk) 22:08, 30 April 2016 (UTC)
 * - valign="bottom"
 * style="padding: 0 1em"|[[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]]
 * style="padding: 0 1em"|[[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]]
 * style="padding: 0 1em"|[[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]]
 * style="padding: 0 1em"|[[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:GrayDot.svg|16px|*]] [[Image:WhiteDot.svg|16px|*]]
 * 12+1||22+2||32+3||42+4
 * }
 * }
 * What do you think this adds relative to the existing image? —David Eppstein (talk) 22:17, 30 April 2016 (UTC)

Merge with triangular numbers: they are just their doubles.
Nth pronic number is just the nth triangular number times 2. — Preceding unsigned comment added by Santropedro (talk • contribs)
 * It's also the nth square number plus its square root. Should we merge with square numbers then, too? —David Eppstein (talk) 06:56, 1 August 2019 (UTC)

Vacuous statement
I removed this bit: If $n$ is a pronic number, then the following is true:
 * $$ \lfloor{\sqrt{n}}\rfloor \cdot \lceil{\sqrt{n}}\rceil = n $$

If x = a x b, then root(x) is equal to a or b if they are equal, and somewhere between a and b if they are different. So obviously if a and b differ by 1, the root is somewhere between then, and rounding the root down gives one, rounding it up gives the other. Imaginatorium (talk) 19:21, 30 November 2020 (UTC)
 * It's an easy-to-prove statement, based on the argument you give, but it's not vacuous. It describes a property that is not true of most other numbers (although it is of course also true of the squares). —David Eppstein (talk) 20:23, 30 November 2020 (UTC)

Cuisenaire rods
Are the illustrations with Cuisenaire rods actually helpful to some users in demonstrating or explaining various properties? (For me, they are more befuddling than anything else.) IMO, if we use images, a better use is the illustration of two equal triangular configurations combining to form an $n$ by $n+1$ rectangular configuration. --Lambiam 14:28, 1 March 2022 (UTC)
 * I agree with you, both that Hyacinth's Cuisenaire images are confusing and that the two-triangle image is a better choice. —David Eppstein (talk) 17:05, 1 March 2022 (UTC)
 * ✅Rods are out, balls it is. --Lambiam 13:11, 6 March 2022 (UTC)