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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.
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 ...
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).
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.
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.
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.
64 = 34 + 21 + 5 + 3 + 1 64 = 34 + 13 + 8 + 5 + 3 + 1. but these are not Zeckendorf representations because 34 and 21 are consecutive Fibonacci numbers, as are 5 and 3. For any given positive integer, its Zeckendorf representation can be found by using a greedy algorithm, choosing the largest possible Fibonacci number at each stage.
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers