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In decimal, the number of two-digit prime numbers is twenty-one (a base in which 21 is the fourteenth Harshad number). [8] [9] It is the smallest non-trivial example in base ten of a Fibonacci number (where 21 is the 8th member, as the sum of the preceding terms in the sequence 8 and 13) whose digits (2, 1) are Fibonacci numbers and whose digit ...
The list on the right shows the numbers 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 (the Fibonacci sequence). The 2, 8, and 9 resemble Arabic numerals more than Eastern Arabic numerals or Indian numerals. The Liber Abaci or Liber Abbaci [1] (Latin for "The Book of Calculation") was a 1202 Latin work on arithmetic by Leonardo of Pisa ...
The number in the n-th month is the n-th Fibonacci number. [21] The name "Fibonacci sequence" was first used by the 19th-century number theorist Édouard Lucas. [22] Solution to Fibonacci rabbit problem: In a growing idealized population, the number of rabbit pairs form the Fibonacci sequence.
All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers (): Numbers that correspond to points along a line. They can be positive, negative, or zero. All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational.
The n-Fibonacci constant is the ratio toward which adjacent -Fibonacci numbers tend; it is also called the n th metallic mean, and it is the only positive root of =. For example, the case of n = 1 {\displaystyle n=1} is 1 + 5 2 {\displaystyle {\frac {1+{\sqrt {5}}}{2}}} , or the golden ratio , and the case of n = 2 {\displaystyle n=2} is 1 + 2 ...
The golden ratio was called the ... The ratio of Fibonacci numbers ... in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the ...
A positive integer sequence is sometimes called multiplicative, if a nm = a n a m for all pairs n, m such that n and m are coprime. [8] In other instances, sequences are often called multiplicative, if a n = na 1 for all n. Moreover, a multiplicative Fibonacci sequence [9] satisfies the recursion relation a n = a n−1 a n−2.
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.
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related to: is 21 a fibonacci number in algebra 2 is called