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The Flint Hills series is the series S_1=sum_(n=1)^infty(csc^2n)/(n^3) (Pickover 2002, p. 59). It is not known if this series converges, since csc^2n can have sporadic large ...

It is always possible to write a sum of sinusoidal functions f(theta)=acostheta+bsintheta (1) as a single sinusoid the form f(theta)=ccos(theta+delta). (2) This can be done ...

A harmonic series is a continued fraction-like series [n;a,b,c,...] defined by x=n+1/2(a+1/3(b+1/4(c+...))) (Havil 2003, p. 99). Examples are given in the following table. c ...

A number which is simultaneously a heptagonal number Hep_n and hexagonal number Hex_m. Such numbers exist when 1/2n(5n-3)=m(2m-1). (1) Completing the square and rearranging ...

A number which is simultaneously a heptagonal number H_n and pentagonal number P_m. Such numbers exist when 1/2n(5n-3)=1/2m(3m-1). (1) Completing the square and rearranging ...

A number which is simultaneously a heptagonal number H_n and triangular number T_m. Such numbers exist when 1/2n(5n-3)=1/2m(m+1). (1) Completing the square and rearranging ...

The Herschel nonahedron is a canonical polyhedron whose skeleton is the Herschel graph. It has 11 vertices, 18 edges, and 9 faces. Of the edges, 6 are short and 12 are long. ...

Honaker's problem asks for all consecutive prime number triples (p,q,r) with p<q<r such that p|(qr+1). Caldwell and Cheng (2005) showed that the only Honaker triplets for ...

An inverse permutation is a permutation in which each number and the number of the place which it occupies are exchanged. For example, p_1 = {3,8,5,10,9,4,6,1,7,2} (1) p_2 = ...

The numbers defined by the recurrence relation K_(n+1)=1+min(2K_(|_n/2_|),3K_(|_n/3_|)), with K_0=1. The first few values for n=0, 1, 2, ... are 1, 3, 3, 4, 7, 7, 7, 9, 9, ...