# 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

.

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 (sequence A069099 in OEIS)

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

### Other articles related to "centered heptagonal number, centered heptagonal, numbers, number, centered, heptagonal, heptagonal numbers, heptagonal number":

Centered Heptagonal Number - 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.. ... (sequence A144974 in OEIS) and centered heptagonal twin prime numbers are 43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651.. ...
8000 (number) - Selected Numbers in The Range 8001–8999
8001 – triangular number 8002 – Mertens function zero 8011 – Mertens function zero 8012 – Mertens function zero 8017 – Mertens function zero 8021 ... pair (first definition) with 8911 ... – Carmichael number, triangular number 8926 – centered heptagonal number 8944 – sum of the cubes of the first seven primes 8951 – Sophie Germain prime 8963 – safe ...
3000 (number) - Selected Numbers in The Range 3001–3999
... 3003 – triangular number, only number known to appear eight times in Pascal's triangle no number is known to appear more than eight times other than 1 ... of the cubes of the first ten integers, centered octagonal number 3045 – sum of the integers 196 to 210 and sum of the integers 211 to 224 3046. 3249 – 57 2, centered octagonal number, member of a Ruth–Aaron pair with 3248 under second definition 3256 – centered heptagonal number 3266 ...
Heptagonal Pyramidal Number
... A heptagonal pyramidal number is the sum of the first few heptagonal numbers ... The heptagonal number for n can be calculated by adding up the heptagonal numbers for 1 to n, or by using the formula n(n + 1)(5n - 2)/6 ... The first few heptagonal pyramidal numbers are ...

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