A001695 a(n) = H_n(2,n) where H_n is the n-th hyperoperator. (Formerly M2352 N0929)

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

Table of n, a(n) for n=0..4.

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.

R. G. Wilson v, Letter to N. J. A. Sloane, Jan. 1989

R. G. Wilson v, Letters to BYTE Magazine (1988) and N. J. A. Sloane (1994)

Index entries for sequences related to 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

Cf. A014221, A046859, A054871.

Sequence in context: A286125 A180169 A154714 * A019676 A246726 A019900

Adjacent sequences: A001692 A001693 A001694 * A001696 A001697 A001698

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