

A189896


Weak Ackermann numbers: H_n(n,n) where H_n is the nth hyperoperator.


8




OFFSET

0,2


COMMENTS

The next term, a(4), would have approximately 5.4 * 10^307 digits.  M. F. Hasler, Jun 17 2012


LINKS

Table of n, a(n) for n=0..3.
M. H. Löb and S. S. Wainer, Hierarchies of numbertheoretic functions. I, Archive for Mathematical Logic 13:12 (1970), pp. 3951.
Wikipedia, Hyperoperation.
Wikipedia, Ackermann function


FORMULA

a(n) = H_n(n, n), where H_n the hyperoperation indexed by n.


EXAMPLE

a(0) = succ(0) = 0 + 1 = 1, because the zeroth hyperoperation is successor.
a(1) = 1 + 1 = 2, because the first hyperoperation is addition.
a(2) = 2 * 2 = 4, because the second hyperoperation is multiplication.
a(3) = 3^3 = 27, because the third hyperoperation is exponentiation.
a(4) = 4^4^4^4 = 4^(4^(4^4)) = 4^(4^256), because the fourth hyperoperation is tetration. The term is too big to be included: log_2(a(4)) = 2^513.


CROSSREFS

For H_n(x,x) with fixed x, cf. A054871 (x=3, shifted), A141044 (x=1), A253855 (x=4, shifted), A255176 (x=2), A256131 (x=10, shifted).  Danny Rorabaugh, Oct 20 2015
Cf. A271553 ( H_n1(n,n) ).  Natan Arie' Consigli, Apr 10 2016
Sequence in context: A240040 A088888 A102996 * A095182 A104465 A175759
Adjacent sequences: A189893 A189894 A189895 * A189897 A189898 A189899


KEYWORD

nonn,bref


AUTHOR

Max Sills, Apr 30 2011


EXTENSIONS

"Weak" added to definition by Natan Arie' Consigli, Apr 18 2015


STATUS

approved



