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  2. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    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.

  3. Generalizations of Fibonacci numbers - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of...

    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 number, a tetranacci number if the number has four digits, etc. The first few repfigits are:

  4. Fibonacci group - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_group

    From a group and a field (or more generally a ring), the group ring [] is defined as the set of all finite formal -linear combinations of elements of − that is, an element of [] is of the form =, where = for all but finitely many so that the linear combination is finite.

  5. Fibonacci prime - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_prime

    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]

  6. Pisano period - Wikipedia

    en.wikipedia.org/wiki/Pisano_period

    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.

  7. Liber Abaci - Wikipedia

    en.wikipedia.org/wiki/Liber_Abaci

    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.

  8. Integer sequence - Wikipedia

    en.wikipedia.org/wiki/Integer_sequence

    An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.

  9. Fibonacci coding - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_coding

    To encode an integer N: . Find the largest Fibonacci number equal to or less than N; subtract this number from N, keeping track of the remainder.; If the number subtracted was the i th Fibonacci number F(i), put a 1 in place i − 2 in the code word (counting the left most digit as place 0).