login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192330 Minimum number of endpoints of a tree so that there exists a zero-entropy map defined on it having a period n orbit. 1
1, 2, 3, 2, 5, 3, 7, 2, 6, 5, 11, 3, 13, 7, 10, 2, 17, 6, 19, 5, 14, 11, 23, 3, 20, 13, 15, 7, 29, 10, 31, 2, 22, 17, 28, 6, 37, 19, 26, 5, 41, 14, 43, 11, 25, 23, 47, 3, 42, 20, 34, 13, 53, 15, 44, 7, 38, 29, 59, 10, 61, 31, 35, 2, 52, 22, 67, 17, 46, 28, 71, 6, 73, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The topological entropy of a continuous map from a compact metric space into itself is a quantitative measure of the complexity of the dynamical system defined by the iteration of the map. See Adler, Konheim, McAndrew reference.
LINKS
R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319.
E. Barrabés, D. Juher, The minimum tree for a given zero entropy period, Int. J. Math. Math. Sci. 2005:19 (2005), pp. 3025-3033.
FORMULA
a(n) = n - Sum_{i=2..k} Product_{j=i..k} s_j, where n = s_1*s_2*...*s_k with s_i primes and s_i <= s_{i+1}.
EXAMPLE
a(2^n)=2 for n > 0, a(p)=p for p prime, a(k*2^j) = a(k) for k > 0, j >= 0.
PROG
(Magma) A192330:=func< n | n-s where s:=w eq [] select 0 else &+w where w:=[ &*[ v[i]: i in [k..#v] ]: k in [2..#v] ] where v:=&cat[ [ f[j, 1]: i in [1..f[j, 2]] ]: j in [1..#f] ] where f:=Factorization(n) >; [ A192330(n): n in [1..75] ]; // Klaus Brockhaus, Jul 02 2011
(PARI) A192330(n)=
{local(f=factor(n), v=[], k, s); for(j=1, #f[, 2], for(i=1, f[j, 2], v=concat(v, f[j, 1]))); k=#v; s=sum(i=2, k, prod(j=i, k, v[j])); n-s}
vector(75, n, A192330(n)) \\ Klaus Brockhaus, Jul 02 2011
CROSSREFS
Cf. A006948 (zero-entropy permutations of length n), A109395 (denominator of phi(n)/n, phi(n)=A000010(n) is the Euler totient function).
Sequence in context: A303077 A347619 A164858 * A320028 A327076 A215041
KEYWORD
nonn
AUTHOR
David Juher, Jun 28 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)