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<p>198.36.94.34: </p> <hr /> <div>[[Image:Centered heptagonal number.svg|240px|right]]<br /> <br /> 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 <br /> <br /> :&lt;math&gt;{7n^2 - 7n + 2}\over2&lt;/math&gt;.<br /> <br /> This can also be calculated by multiplying the [[triangular number]] for (''n'' - 1) by 7, then adding 1.<br /> <br /> The first few centered heptagonal numbers are<br /> <br /> [[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}}<br /> <br /> Centered heptagonal numbers alternate parity in the pattern odd-even-even-odd.<br /> <br /> == Centered heptagonal prime ==<br /> <br /> A '''centered heptagonal prime''' is a centered heptagonal number that is [[prime number|prime]]. The first few centered heptagonal primes are<br /> :43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ... {{OEIS|A144974}}<br /> and centered heptagonal [[twin prime]] numbers are<br /> :43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ... {{OEIS|A144975}}.<br /> <br /> ==See also==<br /> *Regular [[heptagonal number]].<br /> <br /> {{Classes of natural numbers}}<br /> [[Category:Figurate numbers]]</div>

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