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Centered heptagonal number

Centered figurate number that represents a heptagon with a dot in the center

Centered heptagonal number

Centered figurate number that represents a heptagon with a dot in the center

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}\over2.

The first few centered heptagonal numbers are

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

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, ...

The centered heptagonal twin prime numbers are :43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ...

References

References

  1. {{cite OEIS. A069099. Centered heptagonal numbers
  2. {{cite OEIS. A144974. Centered heptagonal prime numbers
  3. {{cite OEIS. A144975. Centered heptagonal twin prime numbers
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