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The sum-of-factorial powers function is defined by sf^p(n)=sum_(k=1)^nk!^p. (1) For p=1, sf^1(n) = sum_(k=1)^(n)k! (2) = (-e+Ei(1)+pii+E_(n+2)(-1)Gamma(n+2))/e (3) = ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

Mastermind is a simple two-player code-breaking board game invented in 1970 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert. It may have been ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

Find the m×n array of single digits which contains the maximum possible number of primes, where allowable primes may lie along any horizontal, vertical, or diagonal line. For ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

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 ...

The Taniyama-Shimura conjecture, since its proof now sometimes known as the modularity theorem, is very general and important conjecture (and now theorem) connecting topology ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...

Multiply all the digits of a number n by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative ...