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Legendre's constant is the number 1.08366 in Legendre's guess at the prime number theorem pi(n)=n/(lnn-A(n)) with lim_(n->infty)A(n) approx 1.08366. Legendre first published ...

A set n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). If the sum of ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

A Bland-Altman plot is a data plotting method which simultaneously presents data sets from two different tests in a way that allows for easier determination of whether the ...

A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...

11 11 1 11 2 2 11 2 4 2 11 3 6 6 3 11 3 9 10 9 3 11 4 12 19 19 12 4 11 4 16 28 38 28 16 4 11 5 20 44 66 66 44 20 5 11 5 25 60 110 126 110 60 25 5 1 (1) Losanitsch's triangle ...

A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

The Penrose tiles are a pair of shapes that tile the plane only aperiodically (when the markings are constrained to match at borders). These two tiles, illustrated above, are ...

The absolute difference of two numbers n_1 and n_2 is |n_1-n_2|, where the minus sign denotes subtraction and |x| denotes the absolute value.