@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-CSLTS7XX-H
  skos:prefLabel "centered heptagonal number"@en, "nombre heptagonal centré"@fr ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:inScheme psr: ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_heptagonal_centr%C3%A9>, <https://en.wikipedia.org/wiki/Centered_heptagonal_number> ;
  a skos:Concept ;
  skos:definition """A <b>centered heptagonal number</b> 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 <i>n</i> is given by the formula   <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {7n^{2}-7n+2} \\\\over 2}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mfrac>         <mstyle displaystyle="true" scriptlevel="0">           <mrow class="MJX-TeXAtom-ORD">             <mn>7</mn>             <msup>               <mi>n</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mn>2</mn>               </mrow>             </msup>             <mo>−<!-- − --></mo>             <mn>7</mn>             <mi>n</mi>             <mo>+</mo>             <mn>2</mn>           </mrow>         </mstyle>         <mn>2</mn>       </mfrac>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {7n^{2}-7n+2} \\\\over 2}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4e060c8536f36be8c425e6e20ef9a08fad602c0" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.848ex; height:5.676ex;" alt="{\\\\displaystyle {7n^{2}-7n+2} \\\\over 2}"></span>.</dd></dl> The first few centered heptagonal numbers are 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953 (sequence A069099 in the OEIS).  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Centered_heptagonal_number">https://en.wikipedia.org/wiki/Centered_heptagonal_number</a>)"""@en, """En mathématiques, un <b>nombre heptagonal centré</b> est un nombre figuré polygonal centré qui représente un heptagone avec un point central et tous les autres points entourant le point central en couches heptagonales successives. Le <i>n</i>-ième nombre heptagonal centré (le nombre de couches étant <i>n</i> – 1) s'obtient donc en ajoutant 1 au produit par 7 du (<i>n</i> – 1)-ième nombre triangulaire :  <center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle C_{7,n}=1+7~{\\rac {n(n-1)}{2}}={7n^{2}-7n+2 \\\\over 2}.}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>C</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>7</mn>             <mo>,</mo>             <mi>n</mi>           </mrow>         </msub>         <mo>=</mo>         <mn>1</mn>         <mo>+</mo>         <mn>7</mn>         <mtext> </mtext>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mi>n</mi>               <mo stretchy="false">(</mo>               <mi>n</mi>               <mo>−<!-- − --></mo>               <mn>1</mn>               <mo stretchy="false">)</mo>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mn>7</mn>               <msup>                 <mi>n</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mn>2</mn>                 </mrow>               </msup>               <mo>−<!-- − --></mo>               <mn>7</mn>               <mi>n</mi>               <mo>+</mo>               <mn>2</mn>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle C_{7,n}=1+7~{\\rac {n(n-1)}{2}}={7n^{2}-7n+2 \\\\over 2}.}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b736eb34ca81c6c598d041d7d86471d3f743be84" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:40.035ex; height:5.676ex;" alt="{\\\\displaystyle C_{7,n}=1+7~{\\rac {n(n-1)}{2}}={7n^{2}-7n+2 \\\\over 2}.}"></span></center> Ils forment la suite d'entiers A069099 de l'OEIS : 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, <abbr class="abbr" title="et cetera">etc.</abbr> Leur parité suit le motif impair-pair-pair-impair. La sous-suite de ceux qui sont premiers est 43, 71, 197, <abbr class="abbr" title="et cetera">etc.</abbr> (suite A144974 de l'OEIS).  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_heptagonal_centr%C3%A9">https://fr.wikipedia.org/wiki/Nombre_heptagonal_centr%C3%A9</a>)"""@fr ;
  skos:broader psr:-XRXLKWR1-J .

psr:-XRXLKWR1-J
  skos:prefLabel "nombre polygonal centré"@fr, "centered polygonal numbers"@en ;
  a skos:Concept ;
  skos:narrower psr:-CSLTS7XX-H .