51 relations: Abstract machine, Almost surely, American Mathematical Monthly, American Mathematical Society, Arbitrary-precision arithmetic, Arithmetical hierarchy, Berkeley Open Infrastructure for Network Computing, Binary relation, Bit, Conjecture, Counterexample, Directed graph, Distributed computing, Fractal, Function (mathematics), Function composition, Gödel, Escher, Bach, Graph (mathematics), Hail, Halting problem, Helmut Hasse, If and only if, Integer, Iterated function, Jeffrey Lagarias, John Horton Conway, Lothar Collatz, Mathematics, Mersenne prime, Mertens conjecture, Modular arithmetic, Natural number, P-adic number, Paul Erdős, Pólya conjecture, Power of two, Precomputation, Providence, Rhode Island, Residue-class-wise affine group, Shizuo Kakutani, Skewes' number, Space–time tradeoff, Springer Science+Business Media, Stanislaw Ulam, String (computer science), Syracuse University, Theory of computation, Tree (graph theory), Undecidable problem, University of Strasbourg, ..., Wolfram Demonstrations Project. Expand index (1 more) »

## Abstract machine

An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.

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## Almost surely

In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.

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## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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## American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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## Arbitrary-precision arithmetic

In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system.

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## Arithmetical hierarchy

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them.

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## Berkeley Open Infrastructure for Network Computing

The Berkeley Open Infrastructure for Network Computing (BOINC, pronounced - rhymes with "oink"), an open-source middleware system, supports volunteer and grid computing.

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## Binary relation

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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## Bit

A bit is the basic unit of information in computing and digital communications.

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## Conjecture

In mathematics, a conjecture is a conclusion or proposition based on incomplete information, but for which no proof has been found.

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## Counterexample

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.

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## Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph, or set of vertices connected by edges, where the edges have a direction associated with them.

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## Distributed computing

Distributed computing is a field of computer science that studies distributed systems.

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## Fractal

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.

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## Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

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## Function composition

In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.

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## Gödel, Escher, Bach

Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter.

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## Graph (mathematics)

In mathematics, and more specifically in graph theory, a graph is a representation of a set of objects where some pairs of objects are connected by links.

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## Hail

Hail is a form of solid precipitation.

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## Halting problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running or continue to run forever.

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## Helmut Hasse

Helmut Hasse (25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry (Hasse principle), and to local zeta functions.

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## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first, literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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## Iterated function

In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function with itself a certain number of times.

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## Jeffrey Lagarias

Jeffrey Clark Lagarias (born November, 1949 in Pittsburgh, Pennsylvania, USA) is a mathematician and professor at the University of Michigan.

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## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is a British mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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## Lothar Collatz

Lothar Collatz (July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia.

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## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

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## Mersenne prime

In mathematics, a Mersenne prime is a prime number that is one less than a power of two.

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## Mertens conjecture

In mathematics, the Mertens conjecture is the false statement that the Mertens function M(n) is bounded by √n, which implies the Riemann hypothesis.

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## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus.

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## Natural number

In mathematics, the natural numbers (sometimes called the whole numbers): "whole number An integer, though sometimes it is taken to mean only non-negative integers, or just the positive integers." give definitions of "whole number" under several headwords: INTEGER … Syn. whole number.

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## P-adic number

In mathematics the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems.

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## Paul Erdős

Paul Erdős (Erdős Pál; 26 March 1913 – 20 September 1996) was a Hungarian mathematician.

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## Pólya conjecture

In number theory, the Pólya conjecture stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors.

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## Power of two

In mathematics, a power of two means a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

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## Precomputation

In algorithms, precomputation is the act of performing an initial computation before run time to generate a lookup table that can be used by an algorithm to avoid repeated computation each time it is executed.

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## Providence, Rhode Island

Providence is the capital and most populous city in Rhode Island.

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## Residue-class-wise affine group

In mathematics, specifically in group theory, residue-class-wise affine groups are certain permutation groups acting on \mathbb (the integers), whose elements are bijective residue-class-wise affine mappings.

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## Shizuo Kakutani

was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem.

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## Skewes' number

In number theory, Skewes' number is any of several extremely large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which where π is the prime-counting function and li is the logarithmic integral function.

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## Space–time tradeoff

In computer science,.

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## Springer Science+Business Media

Springer Science+Business Media or Springer is a global publishing company that publishes books, e-books and peer-reviewed journals in science, technical and medical (STM) publishing.

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## Stanislaw Ulam

Stanisław Marcin Ulam (pronounced; 13 April 1909 – 13 May 1984) was a Polish-American mathematician.

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## String (computer science)

In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.

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## Syracuse University

Syracuse University, commonly referred to as Syracuse, 'Cuse, or SU, is a private research university located in Syracuse, New York. The institution's roots can be traced to the Genesee Wesleyan Seminary (later becoming Genesee College), founded by the Methodist Episcopal Church in Lima, New York, in 1831. Following several years of debate over relocating the college to Syracuse, the university was established in 1870, independent of the college. Since 1920, the university has identified itself as nonsectarian, although it maintains a relationship with The United Methodist Church. The campus is located in the University Hill neighborhood of Syracuse, east and southeast of downtown, on one of the larger hills. Its large campus features an eclectic mix of buildings, ranging from nineteenth-century Romanesque Revival structures to contemporary buildings. SU is organized into 13 schools and colleges, with nationally recognized programs in information studies and library science, architecture, communications, business administration,, sport management, public administration, engineering and the College of Arts and Sciences. Syracuse University athletic teams, known as the Orange, participate in 20 intercollegiate sports. SU is a member of the Atlantic Coast Conference for all NCAA Division I athletics, except for women's ice hockey, and the rowing team. SU is also a member of the Eastern College Athletic Conference.

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## Theory of computation

In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm.

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## Tree (graph theory)

In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.

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## Undecidable problem

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.

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## University of Strasbourg

The University of Strasbourg in Strasbourg, Alsace, France, is the second largest university in France (after Aix-Marseille University), with about 46,000 students and over 4,000 researchers.

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## Wolfram Demonstrations Project

The Wolfram Demonstrations Project is hosted by Wolfram Research, whose stated goal is to bring computational exploration to the widest possible audience.

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## Redirects here:

3*n+1, 3*n+1 conjecture, 3*x+1, 3n + 1, 3n + 1 conjecture, 3n 1, 3n 1 problem, 3n+1, 3n+1 problem, 3x + 1, 3x + 1 problem, 3x+1, 3x+1 conjecture, 3x+1 mapping, 3x+1 problem, 3x+1@Home, Collatz Conjecture, Collatz fractal, Collatz graph, Collatz hypothesis, Collatz problem, Collatz sequence, Collatz sequences, HOTPO, Hailstone number, Hailstone numbers, Hailstone sequence, Half or Triple Plus One, Half or triple plus one, Hasse's algorithm, Kakutani problem, Kakutani's problem, Oneness (mathematics), Syracuse algorithm, Syracuse conjecture, Syracuse problem, The 3x + 1 problem, Thwaites conjecture, Ulam problem, Ulam's problem, Wonderous numbers, Wondrous numbers.

## References

[1] https://en.wikipedia.org/wiki/Collatz_conjecture