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A prime divides if and only if p is congruent to ±1 modulo 5, and p divides + if and only if it is congruent to ±2 modulo 5. (For p = 5, F 5 = 5 so 5 divides F 5) . Fibonacci numbers that have a prime index p do not share any common divisors greater than 1 with the preceding Fibonacci numbers, due to the identity: [6]
A Fibonacci sequence of order n is an integer sequence in which each sequence element is the sum of the previous elements (with the exception of the first elements in the sequence). The usual Fibonacci numbers are a Fibonacci sequence of order 2.
In computer science, a generator is a routine that can be used to control the iteration behaviour of a loop.All generators are also iterators. [1] A generator is very similar to a function that returns an array, in that a generator has parameters, can be called, and generates a sequence of values.
An example of a primitive recursive programming language is one that contains basic arithmetic operators (e.g. + and −, or ADD and SUBTRACT), conditionals and comparison (IF-THEN, EQUALS, LESS-THAN), and bounded loops, such as the basic for loop, where there is a known or calculable upper bound to all loops (FOR i FROM 1 TO n, with neither i ...
Plot of the first 10,000 Pisano periods. 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.
Here the fibonorial constant (also called the fibonacci factorial constant [1]) is defined by = = (), where = and is the golden ratio. An approximate truncated value of C {\displaystyle C} is 1.226742010720 (see (sequence A062073 in the OEIS ) for more digits).
A Fibonacci prime is a Fibonacci number that is prime. The first few are: [47] 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... Fibonacci primes with thousands of digits have been found, but it is not known whether there are infinitely many. [48] F kn is divisible by F n, so, apart from F 4 = 3, any Fibonacci prime
As with the Fibonacci numbers, a Pell number P n can only be prime if n itself is prime, because if d is a divisor of n then P d is a divisor of P n. The only Pell numbers that are squares , cubes , or any higher power of an integer are 0, 1, and 169 = 13 2 .