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With the exceptions of 1, 8 and 144 (F 1 = F 2, F 6 and F 12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). [57] As a result, 8 and 144 (F 6 and F 12) are the only Fibonacci numbers that are the product of other Fibonacci numbers. [58]
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 .
In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377. [34] [35] Fibonacci did not ...
A repfigit, or Keith number, is an integer such that, when its digits start a Fibonacci sequence with that number of digits, the original number is eventually reached. An example is 47, because the Fibonacci sequence starting with 4 and 7 (4, 7, 11, 18, 29, 47) reaches 47. A repfigit can be a tribonacci sequence if there are 3 digits in the ...
144 (one hundred [and] forty-four) is the natural number following 143 and preceding 145.It is coincidentally both the square of twelve (a dozen dozens, or one gross.) and the twelfth Fibonacci number, and the only nontrivial number in the sequence that is square.
In number theory, the nth Pisano period, written as π (n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic functions in Fibonacci numbers was noted by Joseph Louis Lagrange in 1774. [1] [2]
In number theory, Carmichael's theorem, named after the American mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind U n (P, Q) with relatively prime parameters P, Q and positive discriminant, an element U n with n ≠ 1, 2, 6 has at least one prime divisor that does not divide any earlier one except the 12th Fibonacci number F(12) = U 12 (1, − ...
Pages in category "Fibonacci numbers" The following 48 pages are in this category, out of 48 total. ... Fibonacci sequence; A. Alphabet (poetry collection) B. Alfred ...