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The primary square is obtained by rotating the root square counter-clockwise by 90 degrees, and replacing the numbers. The resulting square is an associative magic square, in which every pair of numbers symmetrically opposite to the center sum up to the same value, 26. For e.g., 16+10, 3+23, 6+20, etc.
The offset is the index of the first term given. For some sequences, the offset is obvious. For example, if we list the sequence of square numbers as 0, 1, 4, 9, 16, 25 ..., the offset is 0; while if we list it as 1, 4, 9, 16, 25 ..., the offset is 1. The default offset is 0, and most sequences in the OEIS have offset of either 0 or 1.
Printable version; In other projects ... 1 4 9 16 25 36 49 64 81 ... The simplest example of this is the sequence of square triangular numbers.
φ(n) is the number of positive integers not greater than n that are coprime with n. A000010. Lucas numbers L(n) 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... L(n) = L(n − 1) + L(n − 2) for n ≥ 2, with L(0) = 2 and L(1) = 1. A000032. Prime numbers pn. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... The prime numbers pn, with n ≥ 1.
As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction 5 / 7 when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...
Square pyramidal number. Geometric representation of the square pyramidal number 1 + 4 + 9 + 16 = 30. In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci.
Endless sequence of integers. In mathematicsand computer science, Recamán's sequence[1][2]is a well known sequencedefined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.
In bioinformatics, sequence assembly refers to aligning and merging fragments from a longer DNA sequence in order to reconstruct the original sequence. [1] This is needed as DNA sequencing technology might not be able to 'read' whole genomes in one go, but rather reads small pieces of between 20 and 30,000 bases, depending on the technology used. [1]