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A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

Baillie and Wagstaff (1980) and Pomerance et al. (1980, Pomerance 1984) proposed a test (or rather a related set of tests) based on a combination of strong pseudoprimes and ...

Some interesting properties (as well as a few arcane ones not reiterated here) of the number 239 are discussed in Schroeppel (1972). 239 appears in Machin's formula ...

According to the novel The Hitchhiker's Guide to the Galaxy (Adams 1997), 42 is the ultimate answer to life, the universe, and everything. Unfortunately, it is left as an ...

Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

The nth central fibonomial coefficient is defined as [2n; n]_F = product_(k=1)^(n)(F_(n+k))/(F_k) (1) = ...

A sequence of numbers V={nu_n} is complete if every positive integer n is the sum of some subsequence of V, i.e., there exist a_i=0 or 1 such that n=sum_(i=1)^inftya_inu_i ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

A Lucas chain for an integer n>=1 is an increasing sequence 1=a_0<a_1<a_2<...<a_r=n of integers such that every a_k, k>=1, can be written as a sum a_k=a_i+a_j of smaller ...

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. ...