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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 ...

The Ulam sequence {a_i}=(u,v) is defined by a_1=u, a_2=v, with the general term a_n for n>2 given by the least integer expressible uniquely as the sum of two distinct earlier ...

The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

The Wigner 6j-symbols (Messiah 1962, p. 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in ...

Zarankiewicz's conjecture asserts that graph crossing number for a complete bipartite graph K_(m,n) is Z(m,n)=|_n/2_||_(n-1)/2_||_m/2_||_(m-1)/2_|, (1) where |_x_| is the ...

A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...