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A quartic symmetric graph on 30 nodes and 60 edges corresponding to the skeleton of the Archimdean icosidodecahedron, great dodecahemidodecahedron, great icosidodecahedron, ...

Take any positive integer of two digits or more, reverse the digits, and add to the original number. This is the operation of the reverse-then-add sequence. Now repeat the ...

A prime p is said to be a Sophie Germain prime if both p and 2p+1 are prime. The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, ... (OEIS ...

A Mongolian tent graph is defined as the graph obtained from the grid graph P_m square P_n for odd n by adding an extra vertex above the graph and joining every other vertex ...

A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as A_y=ay^3+by^2+cy+d. The volume of such a solid is the same ...

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

Given two starting numbers (a_1,a_2), the following table gives the unique sequences {a_i} that contain no three-term arithmetic progressions. Sloane sequence A003278 1, 2, ...

If P is a pedal point inside a triangle DeltaABC, and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

If equilateral triangles DeltaABE_(AB), DeltaBCE_(BC), and DeltaACE_(AC) are erected externally on the sides of any triangle DeltaABC, then their centers N_(AB), N_(BC), and ...