|
|
A001695
|
|
a(n) = H_n(2,n) where H_n is the n-th hyperoperator.
(Formerly M2352 N0929)
|
|
11
|
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Originally named: An Ackermann function.
For hyperoperator definitions and links, see A054871.
|
|
REFERENCES
|
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
Alternative formula:
With f(x,y)=
{y+1 if x=0
{0 if x=2, y=0
{1 if x>2, y=0
{2 if x=1, y=0
{f(x-1,f(x,y-1)) otherwise
a(n)= f(n,n);
|
|
EXAMPLE
|
a(0) = H_0(2,0) = 0+1 = 1;
a(1) = H_1(2,1) = 2+1 = 3;
a(2) = H_2(2,2) = 2*2 = 4;
a(3) = H_3(2,3) = 2^3 = 8;
a(4) = H_4(2,4) = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536;
a(5) = H_5(2,5) = 2^^^5 = 2^^2^^2^^2^^2 = 2^^2^^2^^4 = 2^^2^^65536 = ....
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|