

A263458


Deal a pack of n cards into two piles and gather them up, n/2 times. All n such that this reverses the order of the deck.


0



4, 6, 12, 22, 28, 30, 36, 46, 52, 60, 70, 78, 100, 102, 108, 126, 148, 150, 156, 166, 172, 180, 190, 196, 198, 222, 228, 238, 262, 268, 270, 276, 292, 310, 316, 348, 358, 366, 372, 382, 388, 396, 420, 430, 438, 460, 462, 478, 486, 502, 508, 540, 556, 598
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

This seems to be A003628(n)1; that is, each element of this sequence is one less than a prime congruent to 5 or 7 modulo 8.


LINKS



EXAMPLE

Take a deck of 52 playing cards. Deal it into two piles, then pick up the first pile and put it on top of the other. Do this 26 times. The order of the deck is reversed, so 52 belongs to this sequence.


PROG

(Sage)
from itertools import cycle
def into_piles(r, deck):
packs = [[] for i in range(r)]
for card, pack in zip(range(1, deck+1), cycle(range(r))):
packs[pack].insert(0, card)
out = sum(packs, [])
return Permutation(out)
def has_reversing_property(deck):
p = power(into_piles(2, deck), deck/2)
return p==into_piles(1, deck)
[i for i in range(2, 400, 2) if has_reversing_property(i)]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



