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 A184166 The level of the lowest leaf of the rooted tree with Matula-Goebel number n. 1
 0, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 3, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Matula-Goebel number of a rooted tree is defined in the following recursive manner: to the one-vertex tree there corresponds the number 1; to a tree T with root degree 1 there corresponds the t-th prime number, where t is the Matula-Goebel number of the tree obtained from T by deleting the edge emanating from the root; to a tree T with root degree m>=2 there corresponds the product of the Matula-Goebel numbers of the m branches of T. REFERENCES F. Goebel, On a 1-1-correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141-143. I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131-142. I. Gutman and Yeong-Nan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 17-22. D. W. Matula, A natural rooted tree enumeration by prime factorization, SIAM Review, 10, 1968, 273. LINKS E. Deutsch, Tree statistics from Matula numbers, arXiv preprint arXiv:1111.4288, 2011 FORMULA a(1)=0; if n is the t-th prime, then a(n) = 1 + a(t); if n is composite, n=rs, then a(n) = min(a(r),a(s)). The Maple program is based on this recursive rule. EXAMPLE a(7)=2 because the rooted tree with Matula-Goebel number 7 is the rooted tree Y (all leaves are at level 2). MAPLE with (numtheory): a:= proc(n) option remember;       if n=1 then 0     elif isprime(n)=true then 1 +a(pi(n))     else min (seq (a(i), i=factorset(n)))       fi     end: seq (a(n), n=1..200); CROSSREFS Cf. A184167. Sequence in context: A089242 A185894 A214180 * A029423 A184169 A176207 Adjacent sequences:  A184163 A184164 A184165 * A184167 A184168 A184169 KEYWORD nonn AUTHOR Emeric Deutsch, Oct 22 2011 STATUS approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)