The New Notation for Hyperoperation of a Sequence

For a sequence a_1, a_2, ..., a_n, we define the exponent, tetration and pentation of a sequence a_n as E_{k=1}^{n} (a_k) = a_1[3]a_2[3]...[3]a_n, T_{k=1}^{n} (a_k) = a_1[4]a_2[4]...[4]a_n, Phi_{k=1}^{n} (a_k) = a_1[5]a_2[5]...[5]a_n. Also, we define the i-th hyperoperation of a sequence a_n as {H_i}_{k=1}^{n} (a_k) = a_1[i]a_2[i]...[i]a_n.

Keywords

Hyperoperation, Sequence

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