196 (one hundred ndninety-six) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...

following 195 and preceding 197.

In mathematics

196 is a

square number In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The u ...

, the square of 14. As the square of a

Catalan number In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Ca ...

, it counts the number of walks of length 8 in the positive quadrant of the integer grid that start and end at the origin, moving diagonally at each step. It is part of a sequence of square numbers beginning 0, 1, 4, 25, 196, ... in which each number is the smallest square that differs from the previous number by a

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...

. There are 196 one-sided heptominoes, the

polyomino A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in pop ...

es made from 7 squares. Here, one-sided means that asymmetric polyominoes are considered to be distinct from their mirror images. A

Lychrel number A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. This process is sometimes called the ''196-algorithm'', after the most famous numb ...

is a

which cannot form a

palindromic number A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palin ...

through the

iterative Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...

process of repeatedly reversing its digits and adding the resulting numbers. 196 is the lowest number

conjecture In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in ...

d to be a Lychrel number in

base 10 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numer ...

; the process has been carried out for over a billion iterations without finding a

palindrome A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words ''madam'' or ''racecar'', the date and time ''11/11/11 11:11,'' and the sentence: "A man, a plan, a canal – Pana ...

, but no one has ever proven that it will never produce one.

References

{{DEFAULTSORT:196 (Number) Arithmetic dynamics Integers

In mathematics

See also

References