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.

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

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

Table of n, a(n) for n=1..54.

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

Sequence in context: A027150 A020141 A049478 * A163776 A050558 A331192

Adjacent sequences: A263455 A263456 A263457 * A263459 A263460 A263461

Keyword

nonn

Author

Christian Perfect, Oct 19 2015

Status

approved