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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>.
 
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 (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 {{OEIS|id=A069099}}
 
Centered heptagonal numbers alternate parity in the pattern odd-even-even-odd.
 
== 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, ... {{OEIS|A144974}}
and centered heptagonal [[twin prime]] numbers are
:43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ... {{OEIS|A144975}}.
 
==See also==
*Regular [[heptagonal number]].
 
{{Classes of natural numbers}}
[[Category:Figurate numbers]]

Latest revision as of 02:30, 26 February 2014

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