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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, ...
[0; 4, 4, 8, 16, 18, 5, 1, 1, 1, 1, 7, 1, 1, 6, 2, 9, 58, 1, 3, 4, …] [OEIS 100] Computed up to 1 011 597 392 terms by E. Weisstein. He also noted that while the Champernowne constant continued fraction contains sporadic large terms, the continued fraction of the Copeland–Erdős Constant do not exhibit this property. [Mw 85]
Name First elements Short description OEIS Kolakoski sequence: 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ... The n th term describes the length of the n th run : A000002: Euler's ...
The unary numeral system is the simplest numeral system to represent natural numbers: [1] to represent a number N, a symbol representing 1 is repeated N times. [2]In the unary system, the number 0 (zero) is represented by the empty string, that is, the absence of a symbol.
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. [1] For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
Using all numbers and all letters except I and O; the smallest base where 1 / 2 terminates and all of 1 / 2 to 1 / 18 have periods of 4 or shorter. 35: Covers the ten decimal digits and all letters of the English alphabet, apart from not distinguishing 0 from O. 36: Hexatrigesimal [57] [58]
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.