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The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...

An antimagic square is an n×n array of integers from 1 to n^2 such that each row, column, and main diagonal produces a different sum such that these sums form a sequence of ...

Based on methods developer in collaboration with M. Leclert, Catalan (1865) computed the constant K=0.915965594177... (OEIS A006752) now known as Catalans' constant to 9 ...

A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing ...

Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

The Copeland-Erdős constant has decimal expansion C=0.23571113... (OEIS A033308). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, 2, ...

Two nonisomorphic graphs can share the same graph spectrum, i.e., have the same eigenvalues of their adjacency matrices. Such graphs are called cospectral. For example, the ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

The golden ratio has decimal expansion phi=1.618033988749894848... (OEIS A001622). It can be computed to 10^(10) digits of precision in 24 CPU-minutes on modern hardware and ...