Centered heptagonal number
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for n is given by the formula
The first few centered heptagonal numbers are
- Centered heptagonal numbers alternate parity in the pattern odd-even-even-odd.
- A heptagonal numbers can expressed as a multiple of a triangular number by 7, plus one:
- is the sum of the integers between n+1 and 3n+1 (including) minus the sum of the integers from 0 to n (including).
Centered heptagonal prime
A centered heptagonal prime is a centered heptagonal number that is prime. The first few centered heptagonal primes are
Due to parity, the centered heptagonal primes are in the form of or .
The centered heptagonal twin prime numbers are
- Regular heptagonal number.