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 A229215 If 1, 2, and 3 represent the three 2D vectors (1,0), (0.5,sqrt(3)/2) and (-0.5,sqrt(3)/2) and -1, -2 and -3 are the negation of these vectors, then this sequence represents Gosper's island. 3
 1, -3, 1, -3, -2, -3, 1, -3, 1, -3, -2, -3, -2, -1, -2, -3, -2, -3, 1, -3, 1, -3, -2, -3, 1, -3, 1, -3, -2, -3, -2, -1, -2, -3, -2, -3, -2, -1, -2, -1, 3, -1, -2, -1, -2, -3, -2, -3, -2, -1, -2, -3, -2, -3, 1, -3, 1, -3, -2, -3, 1, -3, 1, -3, -2, -3, -2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence is generated by the rewriting rules P(1) = 1,-3,1, P(2) = 2,1,2, P(3) = 3,2,3, P(-3) = -3,-2,-3, P(-2) = -2,-1,-2, P(-1) = -1,3,-1. The start is 1,2,3,-1,-2,-3. Notice P(-x)= -P(x), since P(x) is symmetric. Among the starting values, only the initial "1" is relevant for computation of the sequence, the image of the other elements (2,3,-1,-2,-3) becomes "pushed away" to infinity. - M. F. Hasler, Aug 06 2015 LINKS Arie Bos, Index notation of grid graphs, arXiv:1210.7123 [cs.CG], 2012. Wikipedia, Gosper curve EXAMPLE Start with 1,2,3,-1,-2,-3 and you get in the first step 1,-3,1,2,1,2,3,2,3,-1,3,-1,-2,-1,-2,-3,-2,-3 and in the second step 1,-3,1,-3,-2,-3,1,-3,1,2,1,2,1,-3, ... ,-1,-2,-3,-2,-3. With each step the length increases by a factor of 3. PROG (PARI) (P(v)=concat(apply(i->[i, i-sign(i)*4^(i*i<2), i], v))); A229215=P(P(P(P([1])))) \\ To get a(n), ceil(log_3(n)) iterations are required. - M. F. Hasler, Aug 06 2015 CROSSREFS Cf. A229214. Sequence in context: A055189 A106824 A317203 * A123508 A117621 A178055 Adjacent sequences:  A229212 A229213 A229214 * A229216 A229217 A229218 KEYWORD easy,sign AUTHOR Arie Bos, Sep 24 2013 EXTENSIONS Definition corrected by Kerry Mitchell, Aug 06 2015 STATUS approved

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Last modified April 14 19:20 EDT 2021. Contains 342951 sequences. (Running on oeis4.)