About: Graham-Conway number   Sponge Permalink

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The Graham-Conway number is an erroneous version of Graham's number from Conway and Guy's book The Book of Numbers. Using up-arrow notation, it is defined as: \begin{eqnarray*} gc(1) &=& 4 \uparrow\uparrow\uparrow\uparrow 4 \\ gc(k + 1) &=& 4 \underbrace{\uparrow\uparrow\uparrow\cdots\uparrow\uparrow\uparrow}_{gc(k) ext{ arrows}} 4 \\ gc(64) &=& ext{Graham-Conway number} \end{eqnarray*} It can be represented as \(\{4,65,1,2\}\) in BEAF. It is Exactly \(\ [4,4,4,64]\) in the Graham Array Notation. The Graham-Conway number is larger than Graham's number.

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  • Graham-Conway number
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  • The Graham-Conway number is an erroneous version of Graham's number from Conway and Guy's book The Book of Numbers. Using up-arrow notation, it is defined as: \begin{eqnarray*} gc(1) &=& 4 \uparrow\uparrow\uparrow\uparrow 4 \\ gc(k + 1) &=& 4 \underbrace{\uparrow\uparrow\uparrow\cdots\uparrow\uparrow\uparrow}_{gc(k) ext{ arrows}} 4 \\ gc(64) &=& ext{Graham-Conway number} \end{eqnarray*} It can be represented as \(\{4,65,1,2\}\) in BEAF. It is Exactly \(\ [4,4,4,64]\) in the Graham Array Notation. The Graham-Conway number is larger than Graham's number.
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abstract
  • The Graham-Conway number is an erroneous version of Graham's number from Conway and Guy's book The Book of Numbers. Using up-arrow notation, it is defined as: \begin{eqnarray*} gc(1) &=& 4 \uparrow\uparrow\uparrow\uparrow 4 \\ gc(k + 1) &=& 4 \underbrace{\uparrow\uparrow\uparrow\cdots\uparrow\uparrow\uparrow}_{gc(k) ext{ arrows}} 4 \\ gc(64) &=& ext{Graham-Conway number} \end{eqnarray*} It can be represented as \(\{4,65,1,2\}\) in BEAF. It is Exactly \(\ [4,4,4,64]\) in the Graham Array Notation. The Graham-Conway number is larger than Graham's number.
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