A302349 a(n) = F_n(n,n), where F is the Clenshaw-Olver hyper-operation hierarchy.

1, 2, 4, 9, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

Offset: 0

Author

Natan Arie Consigli, Apr 05 2018

Keywords

• nonn

Comments

a(5) is too big to include.

The Clenshaw Olver hyper-operation is a recursive function defined as follows:

F_0(a,b) = b+1

F_n(a,0) = 0

F_n+1(a,b+1) = F_n(a, F_n+1(a, b)), for every nonnegative b and n.

Examples

			F_0(0,0) = 0+1 = 1;
F_1(1,1) = 1+1 = 2;
F_2(2,2) = 2*2 = 4;
F_3(a,b) = 3^3 = 9;
F_4(a,b) = 4[4](4-1) = 4^4^4 = ...
		

Links

• C. W. Clenshaw and F. W. J. Olver, Beyond floating point, Journal of the ACM. 31 (2) April 1984, pp. 319-328.

Crossrefs

Cf. A054871, A189896 (same instance using traditional hyper-operation hierarchy).

Formula

F_1(a,b) = a+b;

F_2(a,b) = ab;

F_3(a,b) = a^b;

F_4(a,b) = a[4](b-1).

a[n]b is the square bracket notation for hyper-operation. See A054871 for details.