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

1, 3, 4, 8, 65536

Offset: 0

Author

N. J. A. Sloane, following a suggestion from Robert G. Wilson v, Aug 31 1994

Keywords

• nonn
• nice

Comments

Originally named: An Ackermann function.

For hyperoperator definitions and links, see A054871.

Examples

			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 = ....
		

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.
• 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

Crossrefs

Cf. A014221, A046859, A054871.

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);

Extensions

Example, formula and Hyperoperator notation by Natan Arie Consigli with Danny Rorabaugh's help, Oct 25 2015