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The equation is named after Edward Wight Washburn; [1] also known as Lucas–Washburn equation, considering that Richard Lucas [2] wrote a similar paper three years earlier, or the Bell-Cameron-Lucas-Washburn equation, considering J.M. Bell and F.K. Cameron's discovery of the form of the equation in 1906. [3]
In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal.Like the related Fibonacci numbers, they are a specific type of Lucas sequence (,) for which P = 1, and Q = −2 [1] —and are defined by a similar recurrence relation: in simple terms, the sequence starts with 0 and 1, then each following number is found by adding the number ...
As of September 2015, the largest confirmed Lucas prime is L 148091, which has 30950 decimal digits. [4] As of August 2022, the largest known Lucas probable prime is L 5466311, with 1,142,392 decimal digits. [5] If L n is prime then n is 0, prime, or a power of 2. [6] L 2 m is prime for m = 1, 2, 3, and 4 and no other known values of m.
Lucas sequences are used in some primality proof methods, including the Lucas–Lehmer–Riesel test, and the N+1 and hybrid N−1/N+1 methods such as those in Brillhart-Lehmer-Selfridge 1975. [ 4 ] LUC is a public-key cryptosystem based on Lucas sequences [ 5 ] that implements the analogs of ElGamal (LUCELG), Diffie–Hellman (LUCDIF), and RSA ...
For example, if n+1 = 44 (= 101100 in binary), then, taking the bits one at a time from left to right, we obtain the sequence of indices to compute: 1 2 = 1, 10 2 = 2, 100 2 = 4, 101 2 = 5, 1010 2 = 10, 1011 2 = 11, 10110 2 = 22, 101100 2 = 44. Therefore, we compute U 1, U 2, U 4, U 5, U 10, U 11, U 22, and U 44. We also compute the same ...
Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
In mathematics, the Fibonacci numbers form a sequence defined recursively by: = {= = + > That is, after two starting values, each number is the sum of the two preceding numbers.
The calculator was superseded, in 1982, by the HP-15C.. Although it is argued the HP-41C (introduced late 1979 and only a matter of months after the HP-34C) was a replacement for the HP-34C, they were in fact differentiated as much by price (the HP-34C being 50% that of the HP-41C) as by functionality and performance (the HP-41C being the first HP LCD-based and module-expandable calculator ...