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A145787
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Number of times you have to move n cards from one pile to another doing one up, one down, until you obtain the initial sequence.
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1
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1, 2, 2, 3, 3, 6, 6, 4, 4, 6, 6, 10, 10, 14, 14, 5, 5, 18, 18, 10, 10, 12, 12, 21, 21, 26, 26, 9, 9, 30, 30, 6, 6, 22, 22, 9, 9, 30, 30, 27, 27, 8, 8, 11, 11, 10, 10, 24, 24, 50, 50, 12, 12, 18, 18, 14, 14, 12, 12, 55, 55, 50, 50, 7, 7, 18, 18, 34, 34, 46, 46
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OFFSET
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1,2
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COMMENTS
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Let's say you have 3 cards (1 - 2 - 3). You move 1, 2 over 1, 3 below 2. Now you have: (2-1-3). Now you repeat the movement: You move 2, 1 over 2, 3 below 2. Now you have: (1-2-3). The same initial scenario. Total 2 moves. With 4 cards you do it in three moves. For 8 cards you need 4 moves. For 16 cards you need 5 moves. I can assume that for 32 cards I will do it in 6 moves. But for 14 or 15 cards you need 14 moves. I don't know how to predict how many moves for n cards...
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LINKS
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FORMULA
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MATHEMATICA
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A019567[n_]:=For[m=1, True, m++, If[AnyTrue[{-1, 1}, Divisible[2^m+#, 4n+1]&], Return[m]]]; (* from A019567 *)
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PROG
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(PARI)
deck(n) = {s = "0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ,; :!?.*%$£€=+-&()[]{}_"; v = Vec(s); ss = ""; for (i=1, n, ss = concat(ss, v[i]); ); return (ss); }
move(cards) = {v = Vec(cards); s = ""; for (i=1, length(v), if (i % 2, s = concat(s, v[i]), s = concat(v[i], s)); ); return (s); }
a(n) = {cardsa = deck(n); cardsb = cardsa; diff = 1; nb = 0; while (diff, cardsb = move(cardsb); diff = (cardsa != cardsb); nb++; ); return (nb); }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Hernan Bonsembiante (hernanbon(AT)tutopia.com), Oct 19 2008
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EXTENSIONS
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STATUS
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approved
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