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Sum of numbers in any row, column, or diagonal of a magic square of order n ≥ 3 ... The radical of a positive integer n is the product of the distinct prime numbers ...
In combinatorial mathematics, a de Bruijn sequence of order n on a size-k alphabet A is a cyclic sequence in which every possible length-n string on A occurs exactly once as a substring (i.e., as a contiguous subsequence). Such a sequence is denoted by B(k, n) and has length k n, which is also the number of distinct strings of length n on A.
For example, the sequence ,, is a subsequence of ,,,,, obtained after removal of elements ,, and . The relation of one sequence being the subsequence of another is a partial order . Subsequences can contain consecutive elements which were not consecutive in the original sequence.
The final result is that the last cell contains all the longest subsequences common to (AGCAT) and (GAC); these are (AC), (GC), and (GA). The table also shows the longest common subsequences for every possible pair of prefixes. For example, for (AGC) and (GA), the longest common subsequence are (A) and (G).
Beginning of the Fibonacci sequence on a building in Gothenburg. In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers.. An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms.
In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of , its subsequence , …, has a low discrepancy.. Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set B is close to proportional to the measure of B, as would happen on average (but not for particular samples) in the case ...
This subsequence has length six; the input sequence has no seven-member increasing subsequences. The longest increasing subsequence in this example is not the only solution: for instance, 0, 4, 6, 9, 11, 15 0, 2, 6, 9, 13, 15 0, 4, 6, 9, 13, 15. are other increasing subsequences of equal length in the same input sequence.
Such composite numbers are called Lucas pseudoprimes. A prime factor of a term in a Lucas sequence which does not divide any earlier term in the sequence is called primitive . Carmichael's theorem states that all but finitely many of the terms in a Lucas sequence have a primitive prime factor. [ 2 ]