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A300402
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Smallest integer i such that TREE(i) >= n.
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2
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1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
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OFFSET
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0,3
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COMMENTS
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The sequence grows very slowly.
A rooted tree is a tree containing one special node labeled the "root".
TREE(n) gives the largest integer k such that a sequence T(1), T(2), ..., T(k) of vertex-colored (using up to n colors) rooted trees, each one T(i) having at most i vertices, exists such that T(i) <= T(j) does not hold for any i < j <= k. - Edited by Gus Wiseman, Jul 06 2020
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LINKS
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EXAMPLE
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TREE(1) = 1, so a(n) = 1 for n <= 1.
TREE(2) = 3, so a(n) = 2 for 2 <= n <= 3.
TREE(3) > A(A(...A(1)...)), where A(x) = 2[x+1]x is a variant of Ackermann's function, a[n]b denotes a hyperoperation and the number of nested A() functions is 187196, so a(n) = 3 for at least 4 <= n <= A^A(187196)(1).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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