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No odd perfect numbers are known; hence, all known perfect numbers are triangular. For example, the third triangular number is (3 × 2 =) 6, the seventh is (7 × 4 =) 28, the 31st is (31 × 16 =) 496, and the 127th is (127 × 64 =) 8128. The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9.
De numeris triangularibus et inde de progressionibus arithmeticis: Magisteria magna is a 38-page mathematical treatise written in the early 17th century by Thomas Harriot, lost for many years, and finally published in facsimile form in 2009 in the book Thomas Harriot's Doctrine of Triangular Numbers: the "Magisteria Magna".
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Angel numbers are repeating number sequences, often used as guides for deeper spiritual exploration. Ranging from 000 to 999 , each sequence carries its own distinct meaning and energy.
Only five other numbers can be expressed as the sum of the cubes of their digits: 0, 1, 370, 371 and 407. [4] It is also a Friedman number, since 153 = 3 × 51. The Biggs–Smith graph is a symmetric graph with 153 edges, all equivalent. Another feature of the number 153 is that it is the limit of the following algorithm: [5] [6] [7]
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Triplet and higher multiple births nosedive. In 2004, of the people younger than 35 who gave birth with the help of IVF, 32.7% delivered twins, and 4.9% delivered triplets, according to doctors at ...
Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...