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
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
a(5) = H_3(a(3), a(4)) = 3^6 = 729
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Woodward, Dec 04 2023
STATUS
approved