Base-dependent integer sequences | Recreational mathematics

Repdigit

In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit.Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (which are repdigits when represented in binary). Repdigits are the representation in base of the number where is the repeated digit and is the number of repetitions. For example, the repdigit 77777 in base 10 is . A variation of repdigits called Brazilian numbers are numbers that can be written as a repdigit in some base, not allowing the repdigit 11, and not allowing the single-digit numbers (or all numbers will be Brazilian). For example, 27 is a Brazilian number because 27 is the repdigit 33 in base 8, while 9 is not a Brazilian number because its only repdigit representation is 118, not allowed in the definition of Brazilian numbers. The representations of the form 11 are considered trivial and are disallowed in the definition of Brazilian numbers, because all natural numbers n greater than two have the representation 11n − 1. The first twenty Brazilian numbers are 7, 8, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 31, 32, 33, ... (sequence in the OEIS). (Wikipedia).

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Related pages

Perfect power | Binary number | Divergence of the sum of the reciprocals of the primes | Four fours | Numerical digit | Recreational mathematics | Goormaghtigh conjecture | Six nines in pi | Repunit prime | Sophie Germain prime | Highly composite number | Wilhelm Ljunggren | Mersenne number | Bateman–Horn conjecture | Natural number | Mersenne prime | Srinivasa Ramanujan | Fermat number | Prime number | Repunit | Diophantine equation | Radix | Trygve Nagell | Decimal | Square number | Palindromic number