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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.
Look-and-say sequence. The lines show the growth of the numbers of digits in the look-and-say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic vertical scale) tend to straight lines whose slopes coincide with Conway's constant. In mathematics, the look-and-say sequence ...
In mathematics and computer science, Recamán's sequence[1][2] is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion. A drawing of the first 75 terms of Recamán's sequence, according with the method of visualization ...
Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes ...
Sequence. An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
(the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description (sequence A000045 in the OEIS). The sequence 0, 3, 8, 15, ... is formed according to the formula n 2 − 1 for the n th term: an explicit definition.
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For example, P(6) = 4, and there are 4 ways to write 6 as a palindromic ordered sum in which no term is 2: 6 ; 3 + 3 ; 1 + 4 + 1 ; 1 + 1 + 1 + 1 + 1 + 1. The number of ways of writing n as an ordered sum in which each term is odd and greater than 1 is equal to P(n − 5). For example, P(6) = 4, and there are 4 ways to write 11 as an ordered sum ...
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