VOOZH about

URL: https://oeis.org/A001695

⇱ A001695 - OEIS

login
A001695
a(n) = H_n(2,n) where H_n is the n-th hyperoperator.
11
1, 3, 4, 8, 65536
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
W. Ackermann, Zum Hilbertschen Aufbau der reellen Zahlen, Math. Ann. 99 (1928), 118-133.
R. C. Buck, Mathematical induction and recursive definitions, Amer. Math. Monthly, 70 (1963), 128-135.
Y. Sundblad, The Ackermann function. A theoretical, computational and formula manipulative study, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 107-119.
Eric Weisstein's World of Mathematics, Ackermann Function.
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
N. J. A. Sloane, following a suggestion from Robert G. Wilson v, Aug 31 1994
EXTENSIONS
Example, formula and Hyperoperator notation by Natan Arie Consigli with Danny Rorabaugh's help, Oct 25 2015
STATUS
approved