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 A264930 a(n) = nn where xy is a right associative hyperoperation. 1
 1, 2, 4, 27, 340282366920938463463374607431768211456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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). ... 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 Cf. A054871, A189896. Sequence in context: A098515 A256451 A059719 * A226347 A305738 A323447 Adjacent sequences:  A264927 A264928 A264929 * A264931 A264932 A264933 KEYWORD nonn AUTHOR Natan Arie Consigli, Nov 29 2015 STATUS approved

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Last modified April 22 10:58 EDT 2021. Contains 343174 sequences. (Running on oeis4.)