Centered heptagonal number

Last updated

Centered heptagonal number.svg

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

Contents

.

The first few centered heptagonal numbers are

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

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, ... [2]

The centered heptagonal twin prime numbers are

43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ... [3]

See also

Related Research Articles

71 (seventy-one) is the natural number following 70 and preceding 72.

43 (forty-three) is the natural number following 42 and preceding 44.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number.

2000 is a natural number following 1999 and preceding 2001.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.

5000 is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic numeral in the English language.

6000 is the natural number following 5999 and preceding 6001.

7000 is the natural number following 6999 and preceding 7001.

8000 is the natural number following 7999 and preceding 8001.

197 is the natural number following 196 and preceding 198.

189 is the natural number following 188 and preceding 190.

253 is the natural number following 252 and preceding 254.

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA069099(Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA144974(Centered heptagonal prime numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA144975(Centered heptagonal twin prime numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.