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As a biprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0); it is the second composite number with an aliquot sum of 11, following 18. 21 is the first member of the second cluster of consecutive discrete semiprimes (21, 22), where the next such cluster is (33, 34, 35).
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A tiling with squares whose side lengths are successive Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13 and 21. The Fibonacci numbers were first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths.
Print/export Download as PDF; Printable version; In other projects ... Pages in category "Fibonacci numbers" The following 48 pages are in this category, out of 48 ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
For instance, 1/3+1/4 = 7/12, so a notation like would represent the number that would now more commonly be written as the mixed number , or simply the improper fraction . Notation of this form can be distinguished from sequences of numerators and denominators sharing a fraction bar by the visible break in the bar.
For instance, the Zeckendorf representation of 19 is 101001 (where the 1's mark the positions of the Fibonacci numbers used in the expansion 19 = 13 + 5 + 1), the binary sequence 101001, interpreted as a binary number, represents 41 = 32 + 8 + 1, and the 19th fibbinary number is 41.
The k-Wall–Sun–Sun primes can be explicitly defined as primes p such that p 2 divides the k-Fibonacci number (()), where F k (n) = U n (k, −1) is a Lucas sequence of the first kind with discriminant D = k 2 + 4 and () is the Pisano period of k-Fibonacci numbers modulo p. [15]