Search Results for ""

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).

A positive even value of n for which phi(x)=n, where phi(x) is the totient function, has no solution. The first few are 14, 26, 34, 38, 50, ... (OEIS A005277).

The sequence of binary digits of the Thue constant, 0.110110111110110111110110110..._2 (OEIS A014578). A recurrence plot of the limiting value of this sequence is illustrated ...

The classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...

The mean triangle area of a triangle picked at random inside a unit cube is A^_=0.15107+/-0.00003, with variance var(A)=0.008426+/-0.000004. The distribution of areas, ...

The golden ratio conjugate, also called the silver ratio, is the quantity Phi = 1/phi (1) = phi-1 (2) = 2/(1+sqrt(5)) (3) = (sqrt(5)-1)/2 (4) = 0.6180339887... (5) (OEIS ...

The odd part Od(n) of a positive integer n is defined by Od(n)=n/(2^(b(n))), where b(n) is the exponent of the exact power of 2 dividing n. Od(n) is therefore the product of ...

The sum of the aliquot divisors of n, given by s(n)=sigma(n)-n, where sigma(n) is the divisor function. The first few values are 0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, ... ...

Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...