login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123121 Length of the n-th Zimin word (A082215(n)). 5
1, 3, 7, 15, 31, 63, 127, 255, 511, 1024, 2050, 4102, 8206, 16414, 32830, 65662, 131326, 262654, 525310, 1050622, 2101246, 4202494, 8404990, 16809982, 33619966, 67239934, 134479870, 268959742, 537919486, 1075838974, 2151677950, 4303355902, 8606711806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The length of the n-th Zimin word on a countably infinite alphabet {x_1, x_2, x_3, ...} with Z_{n+1} = Z_n x_{n+1} Z_n (as opposed to the use of base 10 in A082215) is 2^n-1. - Danny Rorabaugh, Mar 12 2015

REFERENCES

M. Lothaire, Algebraic combinatorics on words, Cambridge University Press, Cambridge, 2002.

LINKS

Table of n, a(n) for n=1..33.

J. Cooper and D. Rorabaugh, Bounds on Zimin Word Avoidance, arXiv:1409.3080 [math.CO]; Congressus Numerantium, 222 (2014), 87-95.

L. J. Cummings and M. Mays, A one-sided Zimin construction, Electron. J. Combin. 8 (2001), #R27.

A. I. Zimin, Blocking sets of terms, Math. USSR Sbornik, 47 (1984), No. 2, 353-364.

FORMULA

a(n) = 2*a(n-1) + ceiling(log_10(n+1)).

G.f.: sum(j>=1, x^(10^j))/(1-3*x+2*x^2). - Robert Israel, Sep 18 2014

EXAMPLE

The Zimin words are defined by Z_1 = 1, Z_n = Z_{n-1}nZ_{n-1}.

So the Zimin words are 1, 121, 1213121, 121312141213121 ...

MAPLE

A[1]:= 1:

for i from 2 to 100 do A[i]:= 2*A[i-1]+ilog10(i+1) od:

seq(A[i], i=1..100); # Robert Israel, Sep 18 2014

PROG

(MAGMA) [n le 1 select 1 else 2*Self(n-1) + Ceiling(Log(n+1)/Log(10)): n in [1..40]]; // Vincenzo Librandi, Sep 26 2015

CROSSREFS

Cf. A082215.

Sequence in context: A225883 A255047 A168604 * A117060 A178460 A057613

Adjacent sequences:  A123118 A123119 A123120 * A123122 A123123 A123124

KEYWORD

nonn,base

AUTHOR

Dmitry Kamenetsky, Sep 29 2006

EXTENSIONS

More terms from Vincenzo Librandi, Sep 26 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified June 22 12:24 EDT 2017. Contains 288613 sequences.