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A centered triangular number is a centered polygonal number consisting of a central dot with three dots around it, and then additional dots in the gaps between adjacent dots. ...

Let (K,|·|) be a non-Archimedean field. Its valuation ring R is defined to be R={x in K:|x|<=1}. The valuation ring has maximal ideal M={x in K:|x|<1}, and the field R/M is ...

A number defined by b_n=b_n(0), where b_n(x) is a Bernoulli polynomial of the second kind (Roman 1984, p. 294), also called Cauchy numbers of the first kind. The first few ...

The composite number problem asks if for a given positive integer N there exist positive integers m and n such that N=mn. The complexity of the composite number problem was ...

Given a "good" graph G (i.e., one for which all intersecting graph edges intersect in a single point and arise from four distinct graph vertices), the crossing number is the ...

While the Catalan numbers are the number of p-good paths from (n,n) to (0,0) which do not cross the diagonal line, the super Catalan numbers count the number of lattice paths ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

Highly composite numbers are numbers such that divisor function d(n)=sigma_0(n) (i.e., the number of divisors of n) is greater than for any smaller n. Superabundant numbers ...

Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...