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A positive integer n>1 is quiteprime iff all primes p<=sqrt(n) satisfy |2[n (mod p)]-p|<=p+1-sqrt(p). Also define 2 and 3 to be quiteprimes. Then the first few quiteprimes ...

A positive integer n is a veryprime iff all primes p<=sqrt(n) satisfy {|2[n (mod p)]-p|<=1 very strong; |2[n (mod p)]-p|<=sqrt(p) strong; |2[n (mod p)]-p|<=p/2 weak. (1) The ...

The Dyck graph is unique cubic symmetric graph on 32 nodes, illustrated above in a number of embeddings. It is denoted F_(032)A in the Foster census of cubic symmetric graphs ...

An Eulerian graph is a graph containing an Eulerian cycle. The numbers of Eulerian graphs with n=1, 2, ... nodes are 1, 1, 2, 3, 7, 15, 52, 236, ... (OEIS A133736), the first ...

The line R[s]=1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first ...

The EKG sequence is the integer sequence having 1 as its first term, 2 as its second, and with each succeeding term being the smallest number not already used that shares a ...

The center of a graph G is the set of vertices of graph eccentricity equal to the graph radius (i.e., the set of central points). In the above illustration, center nodes are ...

A merge sort (or collation sort) is the combination of two or more ordered lists into a single ordered list (Knuth 1998, p. 158). Merge sorting was one of the first methods ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

A pair of numbers m and n such that sigma^*(m)=sigma^*(n)=m+n, where sigma^*(n) is the unitary divisor function. Hagis (1971) and García (1987) give 82 such pairs. The first ...