A067652 a(n) = H_n(2,3) = H_(n-1)(2,4) where H_n is the n-th hyperoperator.

4, 5, 6, 8, 16, 65536

Offset: 0

Author

Ashley Yakeley (ashley(AT)yakeley.org), Feb 03 2002

Keywords

• nonn
• bref

Comments

Originally named "2 plus 3, twice 3, 2 to the power of 3, etc."

For hyperoperator definitions and links, see A054871.

For nonnegative n, H_(n)(2,3) = H_(n-1)(2,H_(n-1)(2,2)) = H_(n-1)(2,4) or in the clearer square bracket notation: 2[n]3 = 2[n-1]2[n-1]2 = 2[n-1]4. - Natan Arie Consigli, Dec 07 2015

Examples

			H_0(2,3) = 3+1 = 4;
H_1(2,3) = 2+3 = 5;
H_2(2,3) = 2*3 = 6;
H_3(2,3) = 2^3 = 2*2*2 = 2*4 = H_2(2,4) = 8;
H_4(2,3) = 2^^3 = 2^2^2 =  2^4 = H_3(2,4) = 16;
H_5(2,3) = 2^^^3 = 2^^2^^2 = 2^^4 = H_4(2,4) = 2^2^2^2 = 2^16 = 65536;
H_6(2,3) = 2^^^^3 = 2^^^2^^^2 = 2^^^4 = H_5(2,4) = 2^^2^^2^^2 = 2^^65536 = 2^2^...^2^2, with 65536 2's.
		

Crossrefs

Cf. A054871.

Programs

Haskell

f a 0 = 2 + a / f 0 1 = 0 / f 0 n = 1 / f a n = f (f (a-1) n) (n-1)

Extensions

Hyperoperator notation, new initial term, and examples by Danny Rorabaugh, Oct 14 2015

Sequence merged with H_(n)(2,4) by Natan Arie Consigli, Dec 07 2015