KNOWPIA
WELCOME TO KNOWPIA

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. Like square numbers, the digital root in base 10 of a heptagonal number can only be 1, 4, 7 or 9. Five times a heptagonal number, plus 1 equals a triangular number.

A formula for the sum of the reciprocals of the heptagonal numbers is given by:^{[1]}

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*.

The heptagonal root of *x * is given by the formula

which is obtained by using the quadratic formula to solve for its unique positive root *n*.

**^**Beyond the Basel Problem: Sums of Reciprocals of Figurate Numbers