"Carol number" meaning in English

{
  "etymology_text": "First studied by Cletus Emmanuel, who named it after a friend, Carol G. Kirnon.",
  "forms": [
    {
      "form": "Carol numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Carol number (plural Carol numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
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          "source": "w"
        },
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          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2009, The Philosophers' Magazine - Issue 47, page 4",
          "text": "Mathematically, it is actually interesting in all sorts of ways, being both a Keith number and a Carol number.",
          "type": "quotation"
        },
        {
          "ref": "2014, Rajesh Kumar Thakur, The Power of Mathematical Numbers, page 131",
          "text": "[…] 7. There are 47 occurrences of 47 in the first thousand prime numbers. 8. The atomic number of Silver is 47. 9. It is a Carol number. […]",
          "type": "quotation"
        },
        {
          "ref": "2019, Dr. Ir. Maarten Looijen, Over getallen gesproken - Talking about numbers, page 70",
          "text": "In 2007 the largest Carol number was found for n = 253987, consisting of 152916 digits, by using the programs MultiSieve and PrimeFormGW.",
          "type": "quotation"
        },
        {
          "ref": "2021, Elena Deza, Mersenne Numbers And Fermat Numbers, page 136",
          "text": "For n#x3E;2, the binary representation of the n-th Carol number is n-2 consecutive unities, a single zero in the middle, and n#x2B;1 more consecutive unities, or to put it algebraically, #x5C;textstyle#x7B;CN(n)#x3D;#x5C;sum#x5F;#x7B;i#x3D;1,i#x5C;nen#x2B;2#x7D;#x7B;2n#x7D;2#x7B;i-1.}}",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An integer of the form 4ⁿ-2ⁿ⁺¹-1."
      ],
      "id": "en-Carol_number-en-noun-rqSZd7n4",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "integer",
          "integer"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An integer of the form 4ⁿ-2ⁿ⁺¹-1."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Carol number"
}

{
  "etymology_text": "First studied by Cletus Emmanuel, who named it after a friend, Carol G. Kirnon.",
  "forms": [
    {
      "form": "Carol numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Carol number (plural Carol numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English entries with topic categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "en:Mathematics",
        "en:Number theory"
      ],
      "examples": [
        {
          "ref": "2009, The Philosophers' Magazine - Issue 47, page 4",
          "text": "Mathematically, it is actually interesting in all sorts of ways, being both a Keith number and a Carol number.",
          "type": "quotation"
        },
        {
          "ref": "2014, Rajesh Kumar Thakur, The Power of Mathematical Numbers, page 131",
          "text": "[…] 7. There are 47 occurrences of 47 in the first thousand prime numbers. 8. The atomic number of Silver is 47. 9. It is a Carol number. […]",
          "type": "quotation"
        },
        {
          "ref": "2019, Dr. Ir. Maarten Looijen, Over getallen gesproken - Talking about numbers, page 70",
          "text": "In 2007 the largest Carol number was found for n = 253987, consisting of 152916 digits, by using the programs MultiSieve and PrimeFormGW.",
          "type": "quotation"
        },
        {
          "ref": "2021, Elena Deza, Mersenne Numbers And Fermat Numbers, page 136",
          "text": "For n#x3E;2, the binary representation of the n-th Carol number is n-2 consecutive unities, a single zero in the middle, and n#x2B;1 more consecutive unities, or to put it algebraically, #x5C;textstyle#x7B;CN(n)#x3D;#x5C;sum#x5F;#x7B;i#x3D;1,i#x5C;nen#x2B;2#x7D;#x7B;2n#x7D;2#x7B;i-1.}}",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An integer of the form 4ⁿ-2ⁿ⁺¹-1."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "integer",
          "integer"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An integer of the form 4ⁿ-2ⁿ⁺¹-1."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Carol number"
}