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The integer sequence defined by the recurrence P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=3, P(1)=0, P(2)=2. This recurrence relation is the same as that for the ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...

A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral ...

A positive integer n is called a base-b Rhonda number if the product of the base-b digits of n is equal to b times the sum of n's prime factors. These numbers were named by ...

A semiprime, also called a 2-almost prime, biprime (Conway et al. 2008), or pq-number, is a composite number that is the product of two (possibly equal) primes. The first few ...

The Skewes number (or first Skewes number) is the number Sk_1 above which pi(n)<li(n) must fail (assuming that the Riemann hypothesis is true), where pi(n) is the prime ...

Given three noncollinear points, construct three tangent circles such that one is centered at each point and the circles are pairwise tangent to one another. Then there exist ...

The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes. The numbers derive their name from the Hardy-Ramanujan number Ta(2) = ...

The tribonacci numbers are a generalization of the Fibonacci numbers defined by T_1=1, T_2=1, T_3=2, and the recurrence equation T_n=T_(n-1)+T_(n-2)+T_(n-3) (1) for n>=4 ...