Centered nonagonal number

A centered nonagonal number (or centered enneagonal number) is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers.

All even perfect numbers are triangular numbers whose index is an odd Mersenne prime.

[2] Since every Mersenne prime greater than 3 is congruent to 1 modulo 3, it follows that every even perfect number greater than 6 is a centered nonagonal number.

In 1850, Sir Frederick Pollock conjectured that every natural number is the sum of at most eleven centered nonagonal numbers.

[3] Pollock's conjecture was confirmed as true in 2023.