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Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
Even and odd numbers: An integer is even if it is a multiple of 2, and is odd otherwise. Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Alternatively, and for greater numbers, one may say for 1 ⁄ 2 "one over two", for 5 ⁄ 8 "five over eight", and so on. This "over" form is also widely used in mathematics. Fractions together with an integer are read as follows: 1 + 1 ⁄ 2 is "one and a half" 6 + 1 ⁄ 4 is "six and a quarter" 7 + 5 ⁄ 8 is "seven and five eighths"
21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students at a party. [2] [3]
1. Denotes subtraction and is read as minus; for example, 3 – 2. 2. Denotes the additive inverse and is read as minus, the negative of, or the opposite of; for example, –2. 3. Also used in place of \ for denoting the set-theoretic complement; see \ in § Set theory. × (multiplication sign) 1.