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Let F_n be the nth Fibonacci number. Then the sequence {F_n}_(n=2)^infty={1,2,3,5,8,...} is complete, even if one is restricted to subsequences in which no two consecutive ...

A finitely presented group is a group with a finite number of generators and relations. A mathematical joke involving finitely presented groups is given by Renteln and Dundes ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

Let a_n>=0 and suppose sum_(n=1)^inftya_ne^(-an)∼1/a as a->0^+. Then sum_(n<=x)a_n∼x as x->infty. This theorem is a step in the proof of the prime number theorem, but has ...

The heptanacci constant is the limiting ratio of adjacent heptanacci numbers. It is the algebraic number P = (x^7-x^6-x^5-x^4-x^3-x^2-x-1)_1 (1) = 1.99196419660... (2) (OEIS ...

The hexanacci constant is the limiting ratio of adjacent hexanacci numbers. It is the algebraic number P = (x^6-x^5-x^4-x^3-x^2-x-1)_2 (1) = 1.98358284342... (2) (OEIS ...

Let Gamma be an algebraic curve in a projective space of dimension n, and let p be the prime ideal defining Gamma, and let chi(p,m) be the number of linearly independent ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

Hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x is said to be finite iff |x|<n ...

A formula for the generalized Catalan number _pd_(qi). The general formula is (n-q; k-1)=sum_(i=1)^k_pd_(qi)(n-pi; k-i), where (n; k) is a binomial coefficient, although ...