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The fraction of odd values of the partition function P(n) is roughly 50%, independent of n, whereas odd values of Q(n) occur with ever decreasing frequency as n becomes ...
A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...
A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...
A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...
A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...
A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and ...
There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...
In this work, the name Pythagoras's constant will be given to the square root of 2, sqrt(2)=1.4142135623... (1) (OEIS A002193), which the Pythagoreans proved to be ...
What is the maximum number of queens that can be placed on an n×n chessboard such that no two attack one another? The answer is n-1 queens for n=2 or n=3 and n queens ...
The resistance distance between vertices i and j of a graph G is defined as the effective resistance between the two vertices (as when a battery is attached across them) when ...
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