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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112683 For each positive integer n, consider the ternary sequence given initially by x(i) = 0 if 1 <= i < n, x(n) = 1; and thereafter determined by the quadratic recurrence x(i) = x(i-1) + x(i-n)^2 mod 3. Define a(n) to be the smallest positive integer N for which x(N+i) = x(i) for all sufficiently large i. 2
1, 4, 4, 9, 19, 4, 4, 22, 36, 4, 4, 45, 64, 4, 4, 102, 182, 213, 4, 188, 272, 4, 412, 225, 202, 4, 4, 1444, 512, 4, 4, 840, 1237, 4, 1138, 362, 1263, 4, 4, 1536, 672, 1786, 4, 701, 741, 4, 4, 2098, 3921, 5400, 178, 1183, 2348, 4, 7698, 6042, 5091, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Terms computed by Bob Harder.

LINKS

Table of n, a(n) for n=1..59.

S. R. Finch, Periodicity in Sequences Mod 3

EXAMPLE

For example, if n=4, then N=9, since the first 60 terms of x are:

0 0 0 1 1 1 1 2 0 1

2 0 0 1 2 2 2 0 1 2

0 0 1 2 2 2 0 1 2 0

0 1 2 2 2 0 1 2 0 0

1 2 2 2 0 1 2 0 0 1

2 2 2 0 1 2 0 0 1 2

MATHEMATICA

period[lst_List] := Catch[lg = If[Length[lst] <= 5, 2, 40]; lst1 = lst[[1 ;; lg]]; km = Length[lst] - lg; Do[ If[lst1 == lst[[k ;; k+lg-1]], Throw[k-1]]; If[k == km, Throw[0]], {k, 2, km}]]; a[n_] := (ClearAll[x]; x[i_ /; 1 <= i < n] = 0; x[n] = 1; x[i_] := x[i] = Mod[x[i-1] + x[i-n]^2, 3]; xx = Table[x[i], {i, 1, 20000}]; period[xx // Reverse]); Table[a[n], {n, 1, 59}] (* Jean-Fran├žois Alcover, Nov 30 2012 *)

CROSSREFS

Cf. A112684, A112675.

Sequence in context: A214826 A135065 A067553 * A192030 A117879 A069549

Adjacent sequences:  A112680 A112681 A112682 * A112684 A112685 A112686

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 31 2005.

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 04:21 EST 2019. Contains 319323 sequences. (Running on oeis4.)