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A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors (excluding 1). (The primes are excluded since they trivially ...

A snake is an Eulerian path in the d-hypercube that has no chords (i.e., any hypercube edge joining snake vertices is a snake edge). Klee (1970) asked for the maximum length ...

Taniguchi's constant is defined as C_(Taniguchi) = product_(p)[1-3/(p^3)+2/(p^4)+1/(p^5)-1/(p^6)] (1) = 0.6782344... (2) (OEIS A175639), where the product is over the primes ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...

The trinomial triangle is a number triangle of trinomial coefficients. It can be obtained by starting with a row containing a single "1" and the next row containing three 1s ...

A prime p is called a Wolstenholme prime if the central binomial coefficient (2p; p)=2 (mod p^4), (1) or equivalently if B_(p-3)=0 (mod p), (2) where B_n is the nth Bernoulli ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

An n-step Fibonacci sequence {F_k^((n))}_(k=1)^infty is defined by letting F_k^((n))=0 for k<=0, F_1^((n))=F_2^((n))=1, and other terms according to the linear recurrence ...

The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin ...

The finite difference is the discrete analog of the derivative. The finite forward difference of a function f_p is defined as Deltaf_p=f_(p+1)-f_p, (1) and the finite ...