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Find minimal l n such that any set of n residues modulo p can be covered by an arithmetic progression of the length l n. [7]For a given set S of integers find the minimal number of arithmetic progressions that cover S
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
2 Examples. 3 Properties. 4 See also. 5 References. ... The following Python source code tests a sequence of numbers to determine if it is superincreasing: sequence = ...
This is a list of notable integer sequences with links to their entries in the ... 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 ...
Sequences dn + a with odd d are often ignored because half the numbers are even and the other half is the same numbers as a sequence with 2d, if we start with n = 0. For example, 6n + 1 produces the same primes as 3n + 1, while 6n + 5 produces the same as 3n + 2 except for the only even prime 2. The following table lists several arithmetic ...
An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
s 0 is the nearest integer to E 2; s 1 is the nearest integer to E 4; s 2 is the nearest integer to E 8; for s n, take E 2, square it n more times, and take the nearest integer. This would only be a practical algorithm if we had a better way of calculating E to the requisite number of places than calculating s n and taking its repeated square ...
All Fibonacci-like integer sequences appear in shifted form as a row of the Wythoff array; the Fibonacci sequence itself is the first row and the Lucas sequence is the second row. Also like all Fibonacci-like integer sequences, the ratio between two consecutive Lucas numbers converges to the golden ratio .