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

${7n^{2}-7n+2} \over 2$.

This can also be calculated by multiplying the triangular number for (n – 1) by 7, then adding 1.

The first few centered heptagonal numbers are

1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953 Template:OEIS

Centered heptagonal numbers alternate parity in the pattern odd-even-even-odd.

Centered heptagonal prime

A centered heptagonal prime is a centered heptagonal number that is prime. The first few centered heptagonal primes are

43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ... Template:OEIS

and centered heptagonal twin prime numbers are

43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ... Template:OEIS.

See also

• Regular heptagonal number.