Centered heptagonal number
Centered figurate number that represents a heptagon with a dot in the center
title: "Centered heptagonal number" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["figurate-numbers"] description: "Centered figurate number that represents a heptagon with a dot in the center" topic_path: "general/figurate-numbers" source: "https://en.wikipedia.org/wiki/Centered_heptagonal_number" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Centered figurate number that represents a heptagon with a dot in the center ::
::figure[src="https://upload.wikimedia.org/wikipedia/commons/1/13/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
:{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
- {{cite OEIS. A069099. Centered heptagonal numbers
- {{cite OEIS. A144974. Centered heptagonal prime numbers
- {{cite OEIS. A144975. Centered heptagonal twin prime numbers
::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::