@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:-CVDPQB0Q-M
  skos:prefLabel "natural numbers"@en, "entier naturel"@fr ;
  a skos:Concept ;
  skos:narrower psr:-SKZ0RG0W-N .

psr:-FM1M1PDT-5
  skos:prefLabel "suite d'entiers"@fr, "integer sequence"@en ;
  a skos:Concept ;
  skos:narrower psr:-SKZ0RG0W-N .

psr:-SKZ0RG0W-N
  skos:prefLabel "nombre heureux"@fr, "happy number"@en ;
  skos:inScheme psr: ;
  skos:broader psr:-CVDPQB0Q-M, psr:-FM1M1PDT-5 ;
  a skos:Concept ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Happy_number>, <https://fr.wikipedia.org/wiki/Nombre_heureux> ;
  skos:definition """En mathématiques, un entier naturel non nul est un nombre heureux si, lorsqu'on calcule la somme des carrés de ses chiffres dans son écriture en base dix puis la somme des carrés des chiffres du nombre obtenu et ainsi de suite, on aboutit au nombre 1. Un nombre est malheureux lorsque ce n'est pas le cas. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_heureux">https://fr.wikipedia.org/wiki/Nombre_heureux</a>)"""@fr, """In number theory, a <b>happy number</b> is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because <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 1^{2}+3^{2}=10}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mn>1</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <msup>           <mn>3</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>=</mo>         <mn>10</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 1^{2}+3^{2}=10}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ca013c764f3885effc09f853b6d4c170782829e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.697ex; height:2.843ex;" alt="{\\\\displaystyle 1^{2}+3^{2}=10}"></span>, and <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 1^{2}+0^{2}=1}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mn>1</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <msup>           <mn>0</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>=</mo>         <mn>1</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 1^{2}+0^{2}=1}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b06934ac2ddea253bec50193b3c34fcba017bb05" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.535ex; height:2.843ex;" alt="{\\\\displaystyle 1^{2}+0^{2}=1}"></span>. On the other hand, 4 is not a happy number because the sequence starting with <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 4^{2}=16}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mn>4</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>=</mo>         <mn>16</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 4^{2}=16}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/891f0a31ba5eed6c31d8879cd3aa3aa66ecd2ea4" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.64ex; height:2.676ex;" alt="{\\\\displaystyle 4^{2}=16}"></span> and <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 1^{2}+6^{2}=37}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mn>1</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <msup>           <mn>6</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>=</mo>         <mn>37</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 1^{2}+6^{2}=37}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/367797fce61656db15c77b19260210c9cca68331" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.697ex; height:2.843ex;" alt="{\\\\displaystyle 1^{2}+6^{2}=37}"></span> eventually reaches <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 2^{2}+0^{2}=4}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mn>2</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <msup>           <mn>0</mn>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>=</mo>         <mn>4</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 2^{2}+0^{2}=4}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ef1584d5436fda5d753e458f57ea83dfd983503" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.535ex; height:2.843ex;" alt="{\\\\displaystyle 2^{2}+0^{2}=4}"></span>, the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called <b>sad</b> or <b>unhappy</b>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Happy_number">https://en.wikipedia.org/wiki/Happy_number</a>)"""@en ;
  dc:modified "2024-10-18"^^xsd:date .