A367897 - OEIS

A367897

a(1)=1, a(n) = H_(n-2)(a(n-2), a(n-1)) where H_n is the n-th hyperoperator.

1, 2, 3, 6, 729

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OFFSET

1,2

COMMENTS

The sequence follows the hierarchy of arithmetic operations (successorship, addition, multiplication, exponentiation, tetration, ...) with the recurrence a(n-2)?a(n-1)=a(n), where "?" follows the sequence of S (successor), +, *, ^, ^^ (tetration), ...

a(6) (=6^^729) is too large to be represented.

Essentially a Fibonacci generalization: the Fibonacci hyperoperation sequence starting with 1.

LINKS

Table of n, a(n) for n=1..5.

Wikipedia, Binary operation

Wikipedia, Hyperoperation

Wikipedia, Generalizations of Fibonacci numbers

EXAMPLE

a(1)=1, a(2)=S(a(1)), a(3)=a(1)+a(2), a(4)=a(2)*a(3), a(5)=a(3)^a(4), a(6)=a(4)^^a(5), ...a(1) = 1

a(2) = H_0(a(1), a(1)) = 1 + 1 = 2 (successor of 1 = 2)

a(3) = H_1(a(1), a(2)) = 1 + 2 = 3

a(4) = H_2(a(2), a(3)) = 2 * 3 = 6