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A264930 a(n) = n<n>n where x<n>y is a right associative hyperoperation. 1
1, 2, 4, 27, 340282366920938463463374607431768211456 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Define x<n>y recursively as follows (this is a right associative version):
x<0>y = x+1;
x<1>0 = x;
x<2>0 = 0;
x<n>y = ( x<n>(y-1) ) <n-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).
...
LINKS
Wikipedia, Hyperoperations.
EXAMPLE
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.
CROSSREFS
Sequence in context: A098515 A256451 A059719 * A226347 A305738 A323447
KEYWORD
nonn
AUTHOR
Natan Arie Consigli, Nov 29 2015
STATUS
approved

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Last modified April 14 00:20 EDT 2024. Contains 371652 sequences. (Running on oeis4.)