A145787 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.

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

Offset

1,2

Comments

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...

Links

Jon Maiga, Table of n, a(n) for n = 1..1000

Formula

a(n) = A019567(floor(n/2)). - Jon Maiga, Oct 06 2019

Mathematica

A019567[n_]:=For[m=1, True, m++, If[AnyTrue[{-1, 1}, Divisible[2^m+#, 4n+1]&], Return[m]]]; (* from A019567 *)
Table[A019567[Floor[n/2]], {n, 80}] (* Jon Maiga, Oct 06 2019 *)

Prog

(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); }
\\ Michel Marcus, Mar 05 2013

Crossrefs

Cf. A019567.

Sequence in context: A116417 A271410 A196055 * A096111 A358337 A101081

Adjacent sequences: A145784 A145785 A145786 * A145788 A145789 A145790

Keyword

nonn

Author

Hernan Bonsembiante (hernanbon(AT)tutopia.com), Oct 19 2008

Extensions

More terms from Michel Marcus, Mar 05 2013

Status

approved