Search results
Results from the WOW.Com Content Network
Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...
An unpublished computational program written in Pascal called Abra inspired this open-source software. Abra was originally designed for physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra. However, Cadabra has ...
The parity sequence is the same as the sequence of operations. Using this form for f(n), it can be shown that the parity sequences for two numbers m and n will agree in the first k terms if and only if m and n are equivalent modulo 2 k. This implies that every number is uniquely identified by its parity sequence, and moreover that if there are ...
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. It can be used in conjunction with other tools for evaluating sums.
The sequence 0, 3, 8, 15, ... is formed according to the formula n 2 − 1 for the nth term: an explicit definition. Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, (sequence A000396 ...
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 ...
Both binaries and source code are available for SageMath from the download page. If SageMath is built from source code, many of the included libraries such as OpenBLAS, FLINT, GAP (computer algebra system), and NTL will be tuned and optimized for that computer, taking into account the number of processors, the size of their caches, whether there is hardware support for SSE instructions, etc.