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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

Table of n, a(n) for n=1..110.

E. Deutsch, Tree statistics from Matula numbers, arXiv preprint arXiv:1111.4288, 2011

Index entries for sequences related to Matula-Goebel numbers

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.)