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 polygonal numbers are a class of series of Figurate numbers each formed by a central dot surrounded by polygonal layers with a constant number of sides A figurate number is a number that can be represented as a regular and discrete geometric pattern (e Construction A regular heptagon is not constructible with Compass and straightedge but is constructible with a marked Ruler and compass The centered heptagonal number for n is given by the formula

${7n^2 - 7n + 2}\over2$ .

This can also be calculated by multiplying the triangular number for (n - 1) by 7, then adding 1. A triangular number is the sum of the n Natural numbers from 1 to n.

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. Mathematics For any number x: x ·1 = 1· x = x (1 is the multiplicative identity In mathematics 8 is a Composite number, its Proper divisors being 1, 2, and 4. 22 ( twenty-two) is the Natural number following 21 and preceding 23. 43 ( forty-three) is the Natural number following 42 and preceding 44. 71 ( seventy-one) is the Natural number following 70 and preceding 72. 197 is the natural number between 196 and 198. It is also a Prime number. The On-Line Encyclopedia of Integer Sequences ( OEIS) also cited simply as Sloane's, is an extensive searchable Database of Integer sequences

Centered heptagonal prime

A centered heptagonal prime is a centered heptagonal number that is prime. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 The first few centered heptagonal primes are

43, 71, 197, 463, 547, 953, 1471, 1933, . . . .

Centered heptagonal prime

See also