Repdigit
Encyclopedia
In recreational mathematics
, a repdigit is a natural number
composed of repeated instances of the same digit, most often in the decimal numeral system
.
Examples are 11
, 666
, 4444, 77777, and 999999
. All repdigits are palindromic number
s and are multiples of repunit
s. One of the most famous repdigits is 666
, referred to in Christian
Eschatology
as the number of the beast.
Repdigits are a representation of a number in base
represented by 
where 
is the repeated digit and 
is the number of repetitions. For example, the repdigit 77 in base 10 is 
.
The word repdigit is a portmanteau
, formed from repeated digit.
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
, a repdigit is a natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
composed of repeated instances of the same digit, most often in the decimal numeral system
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
.
Examples are 11
11 (number)
11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name...
, 666
666 (number)
666 is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and sixty-six) is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and...
, 4444, 77777, and 999999
Feynman point
The Feynman point is a sequence of six 9s that begins at the 762nd decimal place of the decimal representation of . It is named after physicist Richard Feynman, who once stated during a lecture he would like to memorize the digits of until that point, so he could recite them and quip "nine nine...
. All repdigits are palindromic number
Palindromic number
A palindromic number or numeral palindrome is a 'symmetrical' number like 16461, that remains the same when its digits are reversed. The term palindromic is derived from palindrome, which refers to a word like rotor that remains unchanged under reversal of its letters...
s and are multiples of repunit
Repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler...
s. One of the most famous repdigits is 666
666 (number)
666 is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and sixty-six) is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and...
, referred to in Christian
Christian
A Christian is a person who adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus of Nazareth as recorded in the Canonical gospels and the letters of the New Testament...
Eschatology
Eschatology
Eschatology is a part of theology, philosophy, and futurology concerned with what are believed to be the final events in history, or the ultimate destiny of humanity, commonly referred to as the end of the world or the World to Come...
as the number of the beast.
Repdigits are a representation of a number in base
Radix
In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...
represented by where is the repeated digit and is the number of repetitions. For example, the repdigit 77 in base 10 is .The word repdigit is a portmanteau
Portmanteau word
A portmanteau or portmanteau word is a blend of two words or morphemes into one new word. A portmanteau word typically combines both sounds and meanings, as in smog, coined by blending smoke and fog. More generally, it may refer to any term or phrase that combines two or more meanings...
, formed from repeated digit.