Heptagonal number

In mathematics, a heptagonal number is a figurate number that is constructed by combining heptagons with ascending size.

The n-th heptagonal number is given by the formula The first few heptagonal numbers are: The parity of heptagonal numbers follows the pattern odd-odd-even-even.

A formula for the sum of the reciprocals of the heptagonal numbers is given by:[1] with golden ratio

In analogy to the square root of x, one can calculate the heptagonal root of x, meaning the number of terms in the sequence up to and including x.

for its unique positive root n.