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oitation
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There are 8 letters in OITATION ( A1I1N1O1T1 )
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In mathematics, the Hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations) that starts with the unary operation of successor (n = 0), then continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3), after which the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the nth member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration (n = 4), pentation (n = 5), hexation (n = 6), etc.) and can be written as using n − 2 arrows in Knuth's up-arrow notation. * Each hyperoperation may be understood recursively in terms of the previous one by:* * * * a * [ * n * ] * b * = * * * * * a * [ * n * − * 1 * ] * ( * a * [ * n * − * 1 * ] * ( * a * [ * n * − * 1 * ] * ( * ⋯ * [ * n * − * 1 * ] * ( * a * [ * n * − * 1 * ] * ( * a * [ * n * − * 1 * ] * a * ) * ) * ⋯ * ) * ) * ) * * ⏟ * * * * * b * * * copies of * * * a * * * * , * * n * ≥ * 2 * * * {\displaystyle a[n]b=\underbrace {a[n-1](a[n-1](a[n-1](\cdots [n-1](a[n-1](a[n-1]a))\cdots )))} _{\displaystyle b{\mbox{ copies of }}a},\quad n\geq 2} * It may also be defined according to the recursion rule part of the definition, as in Knuth's up-arrow version of the Ackermann function: * * * * * a * [ * n * ] * b * = * a * [ * n * − * 1 * ] * * ( * * a * [ * n * ] * * ( * * b * − * 1 * * ) * * * ) * * , * * n * ≥ * 1 * * * {\displaystyle a[n]b=a[n-1]\left(a[n]\left(b-1\right)\right),\quad n\geq 1} * This can be used to easily show numbers much ... |