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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 ...
This sequence of numbers of parents is the Fibonacci sequence. The number of ancestors at each level, F n, is the number of female ancestors, which is F n−1, plus the number of male ancestors, which is F n−2. [90] [91] This is under the unrealistic assumption that the ancestors at each level are otherwise unrelated.
Although the resulting Fibonacci sequence dates back long before Leonardo, [9] its inclusion in his book is why the sequence is named after him today. The fourth section derives approximations, both numerical and geometrical, of irrational numbers such as square roots. [10] The book also includes proofs in Euclidean geometry. [11]
For any integer n, the sequence of Fibonacci numbers F i taken modulo n is periodic. The Pisano period, denoted π ( n ), is the length of the period of this sequence. For example, the sequence of Fibonacci numbers modulo 3 begins:
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A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...
When P = 1 and Q = −1, the U n (P,Q) sequence represents the Fibonacci numbers. A Fibonacci pseudoprime is often [2]: 264, [3]: 142, [4]: 127 defined as a composite number n not divisible by 5 for which congruence holds with P = 1 and Q = −1. By this definition, the Fibonacci pseudoprimes form a 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. [34] [35] Fibonacci did not ...