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The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
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, 6 n + 1 produces the same primes as 3 n + 1, while 6 n + 5 produces the same as 3 n + 2 except for the only even prime 2.
Every nontrivial Fibonacci integer sequence appears (possibly after a shift by a finite number of positions) as one of the rows of the Wythoff array. The Fibonacci sequence itself is the first row, and a shift of the Lucas sequence is the second row. [4] See also Fibonacci integer sequences modulo n.
The second column and second row have been filled in with ε, because when an empty sequence is compared with a non-empty sequence, the longest common subsequence is always an empty sequence. LCS ( R 1 , C 1 ) is determined by comparing the first elements in each sequence.
In fact, every real number can be written as the limit of a sequence of rational numbers (e.g. via its decimal expansion, also see completeness of the real numbers). As another example, π is the limit of the sequence (3, 3.1, 3.14, 3.141, 3.1415, ...), which is
Sequence A073502, the magic constant for n × n magic square with prime entries (regarding 1 as a prime) with smallest row sums, is an example of a sequence with offset 3, and A072171, "Number of stars of visual magnitude n." is an example of a sequence with offset −1.
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. [3] The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349 ...