Editing Centered heptagonal number

{{Short description|Centered figurate number that represents a heptagon with a dot in the center}}
{{Use American English|date=March 2021}}
{{Use mdy dates|date=March 2021}}
[[Image:Centered heptagonal number.svg|240px|right]]

A '''centered heptagonal number''' is a [[centered number|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 

:<math>{7n^2 - 7n + 2}\over2</math>.

The first few centered heptagonal numbers are

[[1 (number)|1]], [[8 (number)|8]], [[22 (number)|22]], [[43 (number)|43]], [[71 (number)|71]], [[106 (number)|106]], [[148 (number)|148]], [[197 (number)|197]], 253, 316, 386, 463, 547, 638, 736, 841, 953<ref>{{cite OEIS|A069099|Centered heptagonal numbers}}</ref>

== Centered heptagonal prime ==

A '''centered heptagonal prime''' is a centered heptagonal number that is [[prime number|prime]]. The first few centered heptagonal primes are
:43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ...<ref>{{cite OEIS|A144974|Centered heptagonal prime numbers}}</ref>

The centered heptagonal [[twin prime]] numbers are
:43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ...<ref>{{cite OEIS|A144975|Centered heptagonal twin prime numbers}}</ref>

==See also==
*Regular [[heptagonal number]].

==References==
{{reflist}}

{{Figurate numbers}}
{{Classes of natural numbers}}
[[Category:Figurate numbers]]