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The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...

Lehmer (1938) showed that every positive irrational number x has a unique infinite continued cotangent representation of the form x=cot[sum_(k=0)^infty(-1)^kcot^(-1)b_k], (1) ...

The Markov numbers m are the union of the solutions (x,y,z) to the Markov equation x^2+y^2+z^2=3xyz, (1) and are related to Lagrange numbers L_n by L_n=sqrt(9-4/(m^2)). (2) ...

The minimum spanning tree of a weighted graph is a set of edges of minimum total weight which form a spanning tree of the graph. When a graph is unweighted, any spanning tree ...

A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities contain ...

If an aliquot sequence {s^0(n),s(n),s^2(n),...} for a given n is bounded, it either ends at s(1)=0 or becomes periodic. If the sequence is periodic (or eventually periodic), ...

Cahen's constant is defined as C = sum_(k=0)^(infty)((-1)^k)/(a_k-1) (1) = 0.64341054628... (2) (OEIS A118227), where a_k is the kth term of Sylvester's sequence.

The cumulative count of property P for a sequence S_n={a_1,a_2,...,a_n} is a sequence of counts of the numbers of elements a_i with i<=k that satisfy P for k=1, 2, ..., n. ...

A cumulative product is a sequence of partial products of a given sequence. For example, the cumulative products of the sequence {a,b,c,...}, are a, ab, abc, .... Cumulative ...

A cumulative sum is a sequence of partial sums of a given sequence. For example, the cumulative sums of the sequence {a,b,c,...}, are a, a+b, a+b+c, .... Cumulative sums are ...