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Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted F n ... 12, 19, 31, 50, 81, 131, 212, 343, 555, ... . The ratio of ...
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.
The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Although Fibonacci's Liber Abaci contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century. [30] [31] [32] [33]
A prime p > 5, if p 2 divides the Fibonacci number ... All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages.
For generalized Fibonacci sequences (satisfying the same recurrence relation, but with other initial values, e.g. the Lucas numbers) the number of occurrences of 0 per cycle is 0, 1, 2, or 4. The ratio of the Pisano period of n and the number of zeros modulo n in the cycle gives the rank of apparition or Fibonacci entry point of n .
31 July 2020 4,610,945 61 13×2 15294536 + 1 30 September 2023 4,604,116 62 ... is the nth Fibonacci number. Rank [106] Number Discovery date Decimal digits 1
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 page of the Liber Abaci from the National Central Library.The list on the right shows the numbers 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 (the Fibonacci sequence).