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Let psi = 1+phi (1) = 1/2(3+sqrt(5)) (2) = 2.618033... (3) (OEIS A104457), where phi is the golden ratio, and alpha = lnphi (4) = 0.4812118 (5) (OEIS A002390). Define the ...

The value of the 2^0 bit in a binary number. For the sequence of numbers 1, 2, 3, 4, ..., the least significant bits are therefore the alternating sequence 1, 0, 1, 0, 1, 0, ...

In French and German usage, one milliard equals 10^9=1000000000. American usage does not have a number called the milliard, instead using the term billion to denote 10^9. ...

A triangle with rows containing the numbers {1,2,...,n} that begins with 1, ends with n, and such that the sum of each two consecutive entries being a prime. Rows 2 to 6 are ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

Poker is a card game played with a normal deck of 52 cards. Sometimes, additional cards called "jokers" are also used. In straight or draw poker, each player is normally ...

A number n is called amenable if it can be built up from integers a_1, a_2, ..., a_k by either addition or multiplication such that sum_(i=1)^na_i=product_(i=1)^na_i=n (1) ...

A compact manifold is a manifold that is compact as a topological space. Examples are the circle (the only one-dimensional compact manifold) and the n-dimensional sphere and ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...

The number of empty neighbors of a cluster.