login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..17.

Wikipedia, Grzegorczyk hierarchy

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

Cf. A001477, A059100, A072191.

Sequence in context: A106245 A129568 A177892 * A236433 A117122 A122828

Adjacent sequences:  A341755 A341756 A341757 * A341759 A341760 A341761

KEYWORD

nonn,tabl

AUTHOR

Natan Arie Consigli, Feb 19 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)