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A341758
Table T(n,x) = e_n(x), the Grzegorczyk hierarchy function, read by antidiagonals.
0
0, 1, 2, 2, 3, 2, 3, 6, 6, 2, 4, 11, 38, 38, 2, 5, 18, 1446
OFFSET
0,3
COMMENTS
The function is defined by:
e_0(x,y) = x + y;
e_1(x) = x^2 + 2;
e_n(0) = 2;
e_{n+1}(x+1) = e_n( e_{n+1}(x) );
Here we ignore the variable y so in this case:
e_0(x) = x;
The next two terms are T(4, 1) = T(3, 2) = e_3(2) = (e_1)^38(x) which is a number between 2^(2^38) and 2^(2^39), and is too large to display.
FORMULA
e_{n+1}(x) = (e_n)^x(2).
EXAMPLE
Table T(n,x) = e_n(x):
n\x | 0 1 2 3 4 5 6 …
----+------------------------------------------------------------------
0| 0 1 2 3 4 5 6 … (A001477)
1| 2 3 6 11 18 27 … (A059100)
2| 2 6 38 1446 … (A072191)
3| 2 38 …
4| 2 …
CROSSREFS
KEYWORD
nonn,tabl,more
AUTHOR
Natan Arie Consigli, Feb 19 2021
STATUS
approved