

A161172


a(n) is the order (or period) of the "Yummie" permutation applied to a set of n objects.


2



1, 2, 3, 3, 5, 5, 6, 7, 15, 20, 11, 24, 24, 14, 6, 28, 17, 120, 55, 180, 21, 18, 60, 42, 90, 153, 140, 429, 56, 152, 60, 70, 483, 3640, 180, 272, 72, 1260, 180, 252, 174, 1260, 36, 442, 1404, 660, 47, 496, 240, 481, 48, 98, 570, 572
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OFFSET

1,2


COMMENTS

The Yummie permutation is done as follows. Start with a packet of n cards (numbered 1 to n from top to bottom), and deal them into two piles, first to a spectator (pile A), and then to yourself (pile B), saying "You, me," silently to yourself over and over. Then, pick up pile B and deal again, first to the spectator, thereby adding to the existing pile A, and then to yourself, forming a new pile B. Repeat, picking up the diminished pile B, and dealing "You, me" as before. Eventually, just one card remains in pile B; place it on top of pile A. The sequence of cards in pile A determines the Yummie permutation ("You, me" said fast sounds like "Yummie").


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..2048
Colm Mulcahy, The Yummie Deal and Variations , Card Colm, MAA Online, April 2009


EXAMPLE

a(9) = 15, because when the Yummie permutation is applied to {1,2,3,4,5,6,7,8,9} we get {6,2,4,8,9,7,5,3,1}, which corresponds to the product of a disjoint five cycle and a three cycle, and hence has order 15.


PROG

(PARI)
P(n, i)={if(i%2, n(i\2), P(n\2, (ni)\2+1))}
Follow(s, f)={my(t=f(s), k=1); while(t>s, k++; t=f(t)); if(s==t, k, 0)}
Cycles(n)={my(L=List()); for(i=1, n, my(k=Follow(i, j>P(n, j))); if(k, listput(L, k))); vecsort(Vec(L))}
a(n)={lcm(Cycles(n))} \\ Andrew Howroyd, Apr 28 2020


CROSSREFS

Cf. A051732, A161173, A289386.
Sequence in context: A227065 A010761 A320840 * A093505 A238527 A146071
Adjacent sequences: A161169 A161170 A161171 * A161173 A161174 A161175


KEYWORD

nonn


AUTHOR

Colm Mulcahy, Jun 04 2009


STATUS

approved



