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Extend Hilbert's inequality by letting p,q>1 and 1/p+1/q>=1, (1) so that 0<lambda=2-1/p-1/q<=1. (2) Levin (1937) and Stečkin (1949) showed that (3) and ...

Define F(1)=1 and S(1)=2 and write F(n)=F(n-1)+S(n-1), where the sequence {S(n)} consists of those integers not already contained in {F(n)}. For example, F(2)=F(1)+S(1)=3, so ...

The sequence defined by G(0)=0 and G(n)=n-G(G(n-1)). (1) The first few terms for n=1, 2, ... are 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, ... (OEIS A005206). This can be ...

The pair of sequences defined by F(0)=1, M(0)=0, and F(n) = n-M(F(n-1)) (1) M(n) = n-F(M(n-1)). (2) The first few terms of the "male" sequence M(n) for n=0, 1, ... are 0, 0, ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

Given two topological spaces M and N, place an equivalence relationship on the continuous maps f:M->N using homotopies, and write f_1∼f_2 if f_1 is homotopic to f_2. Roughly ...

A generalization of the Fibonacci numbers defined by the four constants (p,q,r,s) and the definitions H_0=p and H_1=q together with the linear recurrence equation ...

A (presumably autobiographical) character in one of astrophysicist Fred Hoyle's novels opined the following. "I figure that if to be totally known and totally loved is worth ...

By way of analogy with the eban numbers, iban numbers are defined as numbers whose English names do not contain the letter "i" (i.e., "i" is banned). The first few are 1, 2, ...

The radical of an ideal a in a ring R is the ideal which is the intersection of all prime ideals containing a. Note that any ideal is contained in a maximal ideal, which is ...