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In mathematics, trailing zeros are a sequence of 0 in the decimal representation (or more generally, in any positional representation) of a number, after which no other digits follow. Trailing zeros to the right of a decimal point , as in 12.340, don't affect the value of a number and may be omitted if all that is of interest is its numerical ...
A generalization of the self-descriptive numbers, called the autobiographical numbers, allow fewer digits than the base, as long as the digits that are included in the number suffice to completely describe it. e.g. in base 10, 3211000 has 3 zeros, 2 ones, 1 two, and 1 three. Note that this depends on being allowed to include as many trailing ...
Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...
In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f is a number x such that f ( x ) = 0 . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form , root-finding algorithms provide approximations to zeros.
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar.Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.
In these three, sequence types (C arrays, Java arrays and lists, and Lisp lists and vectors) are indexed beginning with the zero subscript. Particularly in C, where arrays are closely tied to pointer arithmetic, this makes for a simpler implementation: the subscript refers to an offset from the starting position of an array, so the first ...
An important application is Newton–Raphson division, which can be used to quickly find the reciprocal of a number a, using only multiplication and subtraction, that is to say the number x such that 1 / x = a. We can rephrase that as finding the zero of f(x) = 1 / x − a. We have f ′ (x) = − 1 / x 2 . Newton's ...
In step one we code "B" which is inside the interval [0.5, 0.83): The binary number "0.10x" is the shortest code that represents an interval that is entirely inside [0.5, 0.83). "x" means an arbitrary bit sequence. There are two extreme cases: the smallest x stands for zero which represents the left side of the represented interval. Then the ...