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A189896 Weak Ackermann numbers: H_n(n,n) where H_n is the n-th hyperoperator. 8
1, 2, 4, 27 (list; graph; refs; listen; history; text; internal format)
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 number-theoretic functions. I, Archive for Mathematical Logic 13:1-2 (1970), pp. 39-51.

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_n-1(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

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Last modified November 20 20:54 EST 2018. Contains 317422 sequences. (Running on oeis4.)