A264930 a(n) = nn where xy is a right associative hyperoperation.

1, 2, 4, 27, 340282366920938463463374607431768211456

Offset: 0

Author

Natan Arie Consigli, Nov 29 2015

Keywords

• nonn

Comments

Define xy recursively as follows (this is a right associative version):

x<0>y = x+1;

x<1>0 = x;

x<2>0 = 0;

xy = ( x(y-1) ) x for n>0 and y>0.

We have:

x<1>y = (...((x<0>y)<0>y)...y)(y nested parenthesis) = x+y;

x<2>y = (...((x<1>y)<1>y)...y)(y nested parenthesis) = x*y;

x<3>y = (...((x<2>y)<2>y)...y)(y nested parenthesis) = x^y;

x<4>y = (...((x<3>y)<3>y)...y)(y nested parenthesis) = (...((x^x)^x)...^x) (a height-y bottom-up tower power, NOT tetration) = x^x^(y-1).

...

Examples

			a(0) = 0+1 = 1;
a(1) = 1+1 = 2;
a(2) = 2*2 = 4;
a(3) = 3^3 = 27;
a(4) = ((4^4)^4)^4 = 340282366920938463463374607431768211456;
a(5) = 5<5>5 = (((((5<4>5)<4>5)<4>5)<4>5)<4>5)<4>5.
		

Links

• Wikipedia, Hyperoperations.

Crossrefs

Cf. A054871, A189896.