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The prime HP(n) reached starting from a number n, concatenating its prime factors, and repeating until a prime is reached. For example, for n=9, 9=3·3->33=3·11->311, so 311 ...

The function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

The sequence of numbers {j_n} giving the number of digits in the three-fold power tower n^(n^n). The values of n^(n^n) for n=1, 2, ... are 1, 16, 7625597484987, ... (OEIS ...

The Kubo-Martin-Schwinger (KMS) condition is a kind of boundary-value condition which naturally emerges in quantum statistical mechanics and related areas. Given a quantum ...

A knot diagram is a picture of a projection of a knot onto a plane. Usually, only double points are allowed (no more than two points are allowed to be superposed), and the ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of ...

Legendre's constant is the number 1.08366 in Legendre's guess at the prime number theorem pi(n)=n/(lnn-A(n)) with lim_(n->infty)A(n) approx 1.08366. Legendre first published ...