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In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit. The term stands for repeated unit and was coined in 1966 by Albert H. Beiler in his book ''Recreations in the Theory of Numbers''. A repunit prime is a repunit that is also a prime number. Primes that are repunits in base 2 are Mersenne primes. == Definition == The base-''b'' repunits are defined as (this ''b'' can be either positive or negative) : Thus, the number ''R''''n''''(b)'' consists of ''n'' copies of the digit 1 in base b representation. The first two repunits base ''b'' for ''n''=1 and ''n''=2 are : In particular, the ''decimal (base-10) repunits'' that are often referred to as simply ''repunits'' are defined as : Thus, the number ''R''''n'' = ''R''''n''''(10)'' consists of ''n'' copies of the digit 1 in base 10 representation. The sequence of repunits base 10 starts with : 1, 11, 111, 1111, 11111, 111111, ... . Similarly, the repunits base 2 are defined as : Thus, the number ''R''''n''''(2)'' consists of ''n'' copies of the digit 1 in base 2 representation. In fact, the base-2 repunits are the well-known Mersenne numbers ''M''''n'' = 2''n'' − 1, they start with :1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, ... 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「repunit」の詳細全文を読む スポンサード リンク
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