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 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 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-François 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

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