Triangle Numbers on Ulam Spiral

A number n is said to be a "Triangle Number" if we can arrange n number of objects into a solid triangle pattern: (1,3,6 and 10 are triangle numbers)

 

The n-th triangle number can be found with n = n* (n+1) / 2.

Therefore, the 3rd tri-number is = 3*(3+1)/2 = 6

Below are some images of triangle numbers (along standard and Mersenne primes) plotted onto a square Ulam Spiral grid.. The Tri-numbers show up in a striking spiral in green points.

 

The image on the right is intended to be zoomed in on in a graphics package.

see the ulam prime spiral page.

 

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