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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.

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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; listen)

	OFFSET	`1,2`
	REFERENCES	`Terms computed by Bob Harder (see the Mathcad site).`
	LINKS	`Mathcad, 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`
	CROSSREFS	`Cf. A112684, A112675.` `Sequence in context: A059815 A135065 A067553 this_sequence A117879 A069549 A118069` `Adjacent sequences: A112680 A112681 A112682 this_sequence A112684 A112685 A112686`
	KEYWORD	`nonn`
	AUTHOR	`njas, Dec 31 2005. Thanks to Jeremy Gardiner for finding this web site.`

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Last modified July 23 17:35 EDT 2008. Contains 142285 sequences.

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