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 A261547 The 3 X 3 X ... X 3 dots problem (3, n times): minimal number of straight lines (connected at their endpoints) required to pass through 3^n dots arranged in a 3 X 3 X ... X 3 grid. 4
 1, 1, 4, 14, 41 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is an n-dimensional generalization of the well-known "Nine Dots Problem". Bounds for this problem, for n >= 5, are: ceiling((3^n + n - 3)/2) <= a(n) <= 42*3^(n - 4) - 1. a(5) is 123, 124 or 125, since 123 is the lower bound calculated as above and 125 is the best solution found as of Aug 06 2018. Except for n < 2, the a(n) represent "outside the box" solutions. LINKS M. Ripà, nxnx...xn Dots Puzzle M. Ripà, The rectangular spiral or the n1 X n2 X ... X nk Points Problem, Notes on Number Theory and Discrete Mathematics, 2014, 20(1), 59-71. M. Ripà, The 3 X 3 X ... X 3 Points Problem solution, Notes on Number Theory and Discrete Mathematics, 2019, 25(2), 68-75. Marco Ripà, The n X n X n Points Problem Optimal Solution Wikipedia, Nine dots puzzle FORMULA a(n) = ceiling((3^n + n - 3)/2), for any n >= 2 (conjectured). EXAMPLE For n=4, a(4) = 41. You cannot touch (the centers of) the 3^4 = 81 dots using fewer than 41 straight lines, following the "Nine Dots Puzzle" basic rules. CROSSREFS Cf. A058992, A225227. Sequence in context: A196480 A326008 A196713 * A237853 A132357 A262875 Adjacent sequences:  A261544 A261545 A261546 * A261548 A261549 A261550 KEYWORD nonn,more,hard AUTHOR Marco Ripà, Aug 24 2015 EXTENSIONS a(4) added by Marco Ripà, Aug 06 2018 STATUS approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)