A213619 Let m be the n-th hyperoperation applied to n (see A189896). a(n) is the m-th hyperoperation applied to n and m.

1, 2, 65536

Offset: 0

Author

Jens Ahlström, Jun 16 2012

Keywords

• nonn
• bref

Comments

Let bn=A189896(n), that is, bn=H_n(n,n), where H_n is the n-th hyperoperation.

Then

a(n) = H_bn(n,bn), hence

a(0) = H_b0(0,b0) = H_1(0,1) = 0+1 = 1,

a(1) = H_b1(1,b1) = H_2(1,2) = 1*2 = 2,

a(2) = H_b2(2,b2) = H_4(2,4) = 2^2^2^2 = 65536, and

a(3) is too large to include here.

Examples

			a(0) = H_H_0(0,0)(0,H_0(0,0)) = H_1(0,1) = 0+1 = 1.
a(1) = H_H_1(1,1)(1,H_1(1,1)) = H_2(1,1+1) = 1*(1+1) = 2.
a(2) = H_H_2(2,2)(2,H_2(2,2)) = H_4(2,2*2) = H_3(2,H_3(2,H_3(2,2))) = 2^2^2^2 = 2^2^4 = 2^16 = 65536.
		

Crossrefs

Cf. A189896.

Formula

a(n) = H_H_n(n,n)(n,H_n(n,n)).