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- Hexagonal_number abstract "A hexagonal number is a figurate number. The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.The formula for the nth hexagonal numberThe first few hexagonal numbers (sequence A000384 in OEIS) are:1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946.Every hexagonal number is a triangular number, but only every other triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repeating every nine terms, is "1 6 6 1 9 3 1 3 9".Every even perfect number is hexagonal, given by the formula where Mp is a Mersenne prime. No odd perfect numbers are known, hence all known perfect numbers are hexagonal.For example, the 2nd hexagonal number is 2×3 = 6; the 4th is 4×7 = 28; the 16th is 16×31 = 496; and the 64th is 64×127 = 8128.The largest number that cannot be written as a sum of at most four hexagonal numbers is 130. Adrien-Marie Legendre proved in 1830 that any integer greater than 1791 can be expressed in this way.Hexagonal numbers can be rearranged into rectangular numbers of size n by (2n−1).Hexagonal numbers should not be confused with centered hexagonal numbers, which model the standard packaging of Vienna sausages. To avoid ambiguity, hexagonal numbers are sometimes called "cornered hexagonal numbers".".
- Hexagonal_number thumbnail Hexagonal_numbers.svg?width=300.
- Hexagonal_number wikiPageExternalLink HexagonalNumber.html.
- Hexagonal_number wikiPageID "494013".
- Hexagonal_number wikiPageRevisionID "604433914".
- Hexagonal_number hasPhotoCollection Hexagonal_number.
- Hexagonal_number subject Category:Figurate_numbers.
- Hexagonal_number type Abstraction100002137.
- Hexagonal_number type Amount105107765.
- Hexagonal_number type Attribute100024264.
- Hexagonal_number type FigurateNumbers.
- Hexagonal_number type Magnitude105090441.
- Hexagonal_number type Number105121418.
- Hexagonal_number type Property104916342.
- Hexagonal_number comment "A hexagonal number is a figurate number.".
- Hexagonal_number label "Hexagonal number".
- Hexagonal_number label "Nombre hexagonal".
- Hexagonal_number label "Numero esagonale".
- Hexagonal_number label "Número hexagonal".
- Hexagonal_number label "Número hexagonal".
- Hexagonal_number label "Sechseckszahl".
- Hexagonal_number label "Zeshoeksgetal".
- Hexagonal_number label "Шестиугольное число".
- Hexagonal_number label "عدد مسدسي".
- Hexagonal_number label "六角数".
- Hexagonal_number label "六邊形數".
- Hexagonal_number sameAs Šestiúhelníkové_číslo.
- Hexagonal_number sameAs Sechseckszahl.
- Hexagonal_number sameAs Número_hexagonal.
- Hexagonal_number sameAs Nombre_hexagonal.
- Hexagonal_number sameAs Numero_esagonale.
- Hexagonal_number sameAs 六角数.
- Hexagonal_number sameAs 육각수_(수학).
- Hexagonal_number sameAs Zeshoeksgetal.
- Hexagonal_number sameAs Número_hexagonal.
- Hexagonal_number sameAs m.02h47t.
- Hexagonal_number sameAs Q1165838.
- Hexagonal_number sameAs Q1165838.
- Hexagonal_number sameAs Hexagonal_number.
- Hexagonal_number wasDerivedFrom Hexagonal_number?oldid=604433914.
- Hexagonal_number depiction Hexagonal_numbers.svg.
- Hexagonal_number isPrimaryTopicOf Hexagonal_number.
