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A sequence produced by the instructions "reverse, add to the original, then sort the digits." For example, after 668, the next iteration is given by 668+866=1534, so the next ...

In 1913, Ramanujan asked if the Diophantine equation of second order 2^n-7=x^2, sometimes called the Ramanujan-Nagell equation, has any solutions other than n=3, 4, 5, 7, and ...

The regular hexagon is the regular polygon with six sides, as illustrated above. The inradius r, circumradius R, sagitta s, and area A of a regular hexagon can be computed ...

Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

A series-reduced tree is a tree in which all nodes have degree other than 2 (in other words, no node merely allows a single edge to "pass through"). Series-reduced trees are ...

Ramanujan calculated mu=1.45136380... (Hardy 1999, Le Lionnais 1983, Berndt 1994), while the correct value is mu=1.45136923488... (OEIS A070769; Derbyshire 2004, p. 114). The ...

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

The Somos sequences are a set of related symmetrical recurrence relations which, surprisingly, always give integers. The Somos sequence of order k, or Somos-k sequence, is ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...