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The Padovan sequence numbers can be written in terms of powers of the roots of the equation [1] = This equation has 3 roots; one real root p (known as the plastic ratio) and two complex conjugate roots q and r. [5] Given these three roots, the Padovan sequence can be expressed by a formula involving p, q and r :
This method uses multiple Dynalign calculations to find a low free energy structure common to any number of sequences. It does not require any sequence identity. any: Yes: Yes: No: sourcecode [69] Murlet: a multiple alignment tool for RNA sequences using iterative alignment based on Sankoff's algorithm with sharply reduced computational time ...
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. [1] [2] Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ 1 or the aliquot sum function s in the following way: [1] = = = > = = = If the s n-1 = 0 condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are convergent, the limit of these ...
Software to align DNA, RNA, protein, or DNA + protein sequences via pairwise and multiple sequence alignment algorithms including MUSCLE, Mauve, MAFFT, Clustal Omega, Jotun Hein, Wilbur-Lipman, Martinez Needleman-Wunsch, Lipman-Pearson and Dotplot analysis. Both: Both: DNASTAR: 1993-2016 MUMmer suffix tree based: Nucleotide: Global: S. Kurtz et ...
TK Solver is a mathematical modeling and problem-solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc. Torch is a deep-learning library with support for manipulation, statistical analysis and presentation of Tensors.
These sequences of natural numbers can again be represented by single natural numbers, facilitating their manipulation in formal theories of arithmetic. Since the publishing of Gödel's paper in 1931, the term "Gödel numbering" or "Gödel code" has been used to refer to more general assignments of natural numbers to mathematical objects.