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 A300402 Smallest integer i such that TREE(i) >= n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 where a sequence T(1), T(2), ..., T(k) of rooted trees, each one assigned a label from a set of n labels and each one having at most i vertices, exists such that T(i) <= T(j) does not hold for any i < j <= k. LINKS Eric Weisstein's World of Mathematics, Rooted Tree Wikipedia, Hyperoperation - Notations Wikipedia, Kruskal's tree theorem EXAMPLE 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). CROSSREFS Cf. A090529, A300403, A300404. Sequence in context: A115230 A304733 A165024 * A211020 A157639 A010096 Adjacent sequences:  A300399 A300400 A300401 * A300403 A300404 A300405 KEYWORD nonn AUTHOR Felix FrÃ¶hlich, Mar 05 2018 STATUS approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)