Uniform number

In Mathematical entertaining, a uniform number , (in English repdigit which comes from repeated digit ) is a Entier naturalness formed by the repetition of only one figure, generally in the system of decimal notation. For example, 8, 11, 22, 4.444,77 777, and 999.999 are uniform numbers.

The classes U K

The uniform numbers are gathered in classes of numbers having the same figure. A class is indicated by the followed letter U figure which composes the numbers that it contains. Thus, the numbers of the class U the 3, also called numbers U 3, are 3, 33, 333,3 333,33 333,333 333…

One of the uniform numbers most known is 666, the Nombre of the animal resulting from the Apocalypse from Saint Jean, of the class U 6.

The numbers U 1 or répunits

The class most frequently used is that gathering the numbers U 1. In English, a U1 number is a repunit (Mot-valise of repeated and links ). This name is due to Albert H. Beiler in 1966. The numbers U 1 are mathematically defined by

\ forall N \ in \ mathbb {NR} ^* \ qquad U_n= {10^n-1 \ over9}.

Thus, the

U_n

number is composed of N copies of figure 1. The continuation of the numbers U 1 starts with 1, 11, 111, 1111… (continuation A002275 in the electronic Encyclopédie of the whole continuations.)

All the uniform numbers are numbers palindromes and multiples of numbers U 1.

External bonds

uniform Numbers on MathWorld

Books

Albert Beiler, Re-creations in the theory off numbers . ISBN 0486210960. Chapter 11, of course.
Paulo Ribenboim, The New Book Off Premium Number Records . ISBN 0387944575.

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