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A035485 Card on top of deck at n-th stage of R. K. Guy's shuffling problem. 21
1, 2, 3, 1, 6, 5, 9, 1, 4, 2, 16, 10, 12, 14, 23, 16, 18, 20, 17, 27, 30, 33, 38, 10, 14, 37, 32, 6, 11, 19, 53, 37, 25, 21, 12, 34, 38, 8, 50, 48, 46, 14, 18, 23, 47, 53, 84, 52, 31, 49, 1, 51, 91, 61, 42, 79, 4, 29, 6, 49, 26, 23, 115, 4, 70, 93, 109, 11, 16, 19, 49, 18, 124, 97, 70, 10, 134, 111, 7, 38, 14, 79, 11, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
At n-th step, pick up top n cards and interlace them with the next n.
Here is the deck after steps 0,1,2,3,4,5:
1,2,3,4,5,6,7,...
2,1,3,4,5,6,7,...
3,2,4,1,5,6,7,...
1,3,5,2,6,4,7,8,9,...
6,1,4,3,7,5,8,2,9,10,...
It is conjectured that eventually every number appears on top of the deck.
See A035491 for (the relevant part of) the deck after the n-th step. - M. F. Hasler, Aug 13 2022
REFERENCES
D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.
D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.
LINKS
Eric Weisstein's World of Mathematics, Perfect Shuffle.
FORMULA
a(n) = A035491(n,1), i.e., the first element of the n-th row of that table, for all n > 0. - M. F. Hasler, Aug 13 2022
PROG
(Python)
def aupton(terms):
alst, deck = [1], list(range(1, 2*terms+1))
for n in range(1, terms+1):
first, next = deck[:n], deck[n:2*n]
deck[0:2*n:2] = next
deck[1:2*n:2] = first
alst.append(deck[0])
return alst
print(aupton(83)) # Michael S. Branicky, Feb 01 2021
(PARI) A035485(n)=A035491_row(n+!n)[1]-!n \\ M. F. Hasler, Aug 13 2022
CROSSREFS
See A035491 for the array, also A035490, A035492.
Sequence in context: A110237 A189970 A076631 * A074306 A294218 A356013
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Jud McCranie
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)