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A067652
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a(n) = H_n(2,3) = H_(n-1)(2,4) where H_n is the n-th hyperoperator.
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2
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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PROG
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(Haskell) f a 0 = 2 + a / f 0 1 = 0 / f 0 n = 1 / f a n = f (f (a-1) n) (n-1)
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CROSSREFS
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KEYWORD
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nonn,bref
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AUTHOR
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Ashley Yakeley (ashley(AT)yakeley.org), Feb 03 2002
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EXTENSIONS
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Hyperoperator notation, new initial term, and examples by Danny Rorabaugh, Oct 14 2015
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STATUS
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approved
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