cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A035494 Order in which record high new cards appear for first time on top of deck in Guy's shuffling problem A035485.

Original entry on oeis.org

1, 2, 3, 6, 9, 16, 23, 27, 30, 33, 38, 53, 84, 91, 115, 124, 134, 157, 178, 222, 241, 267, 277, 298, 323, 368, 378, 407, 438, 450, 495, 496, 542, 546, 555, 561, 576, 581, 598, 619, 646, 665, 703, 750, 774, 782, 806, 860, 862, 864, 905, 909, 937, 976, 1005, 1052, 1056, 1121, 1152, 1197, 1241, 1269, 1316
Offset: 1

Views

Author

N. J. A. Sloane, Wouter Meeussen

Keywords

References

  • D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," 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

Crossrefs

Cf. A035485, A035490, A035491, A035492, A035493, A035500, A035501.

Programs

  • Python
    from itertools import count, islice
def agen(): # generator of terms
    deck = []; record = 1; yield 1
    for n in count(1):
        deck += [2*n-1, 2*n]
        first, next = deck[:n], deck[n:2*n]
        deck[0:2*n:2], deck[1:2*n:2] = next, first
        if deck[0] > record: record = deck[0]; yield record
print(list(islice(agen(), 63))) # Michael S. Branicky, Aug 11 2022

Formula

Monotonic subsequence of A035493.

Extensions

More terms from Jud McCranie

A035492 Position of card 1 after n-th shuffle in Guy's shuffling problem (A035485).

Original entry on oeis.org

1, 2, 4, 1, 2, 4, 8, 1, 2, 4, 8, 16, 7, 14, 28, 25, 17, 34, 31, 23, 5, 10, 20, 40, 31, 11, 22, 44, 31, 3, 6, 12, 24, 48, 27, 54, 35, 70, 63, 47, 13, 26, 52, 17, 34, 68, 43, 86, 75, 51, 1, 2, 4, 8, 16, 32, 64, 13, 26, 52, 104, 85, 45, 90, 51
Offset: 0

Views

Author

Wouter Meeussen

Keywords

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

Crossrefs

Cf. A035485, A035490, A035491, A035493, A035494.

Programs

  • Mathematica
    Transpose[Position[NestList[riguy, {}, 64], 1]][[2]] (* See A035490. *)
  • Python
    from itertools import count, islice
def agen(): # generator of terms
    deck = []; yield 1
    for n in count(1):
        deck += [2*n-1, 2*n]
        first, next = deck[:n], deck[n:2*n]
        deck[0:2*n:2], deck[1:2*n:2] = next, first
        yield deck.index(1) + 1
print(list(islice(agen(), 65))) # Michael S. Branicky, Aug 11 2022

A060750 Step at which card n appears on top of deck for first time in Guy's shuffling problem A035485.

Original entry on oeis.org

3, 1, 2, 8, 5, 4, 78, 37, 6, 11, 28, 12, 349, 13, 383, 10, 18, 16, 29, 17, 33, 210, 14, 133, 32, 60, 19, 106, 57, 20, 48, 26, 21, 35, 97, 217, 25, 22, 13932, 863, 205, 54, 30452, 306, 2591, 40, 44, 39, 49, 38, 51, 47, 30, 252992198, 2253, 101, 112, 246, 402, 119, 53, 139
Offset: 1

Views

Author

David W. Wilson, Apr 22 2001

Keywords

Comments

Card #1 is initially at the top of the deck and next appears at the top of the deck after 3 shuffles. Here we do not accept 0 as a valid number of shuffles and so we say that card #1 first shows up on top after 3 shuffles. A060751 and A060752 also adopt this convention. Alternatively, we can say that card #1 first shows up on top after 0 shuffles; this leads to sequences A035490, A057983, A057984, etc.

References

  • See A035490 for references, links and programs.

Crossrefs

Cf. A035485, A035490, A035491, A035492, A035493, A035494, A060751, A060752.

Programs

  • Python
    def a(n):
  deck = list(range(1, 2*maxcards+1))
  for step in range(1, maxcards+1):
    first, next = deck[:step], deck[step:2*step]
    deck[0:2*step:2] = next
    deck[1:2*step:2] = first
    if deck[0] == n: return step
  return '>' + str(step)
maxcards = 31000
print([a(n) for n in range(1, 54)]) # Michael S. Branicky, Mar 01 2021

A057983 These numbers take a record number of steps to reach the top of the deck in Guy's shuffle (see A035485).

Original entry on oeis.org

1, 2, 3, 4, 7, 13, 15, 39, 43, 54, 1227, 1796, 2674, 3464, 6057, 7650, 17083
Offset: 0

Views

Author

Jud McCranie, Oct 24 2000

Keywords

Comments

See A057984 for the number of steps for these to reach the top of the deck.

Examples

			In Guy's shuffle, 4 takes 8 shuffles to reach the top, no smaller number takes more shuffles, so 4 is in the sequence.

References

  • D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, Springer, 1998, chapter 5.
  • D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.

Crossrefs

Cf. A035485, A035490, A035493, A035494, A057984, A060750-A060752.
A057984 = A035490(A057983).

A057984 These numbers are the record number of steps for the numbers in A057983 to reach the top of the deck in Guy's shuffle (see A035485).

Original entry on oeis.org

0, 1, 2, 8, 78, 349, 383, 13932, 30452, 252992198, 364873753, 850627701, 914514429, 17493745212, 471008431072, 1027221839335, 14568535208344
Offset: 0

Views

Author

Jud McCranie, Oct 24 2000

Keywords

Comments

See A057983 for the numbers that take these number of steps to reach the top of the deck. Gale gives a(12) as 21879255397 (incorrect).

Examples

			In Guy's shuffle, 4 takes 8 shuffles to reach the top, no smaller number takes more shuffles, so 8 is in the sequence.

References

  • D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, Springer, 1998, chapter 5.
  • D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.

Crossrefs

Cf. A035485, A035490, A035493, A035494, A057983, A060750-A060752.
A057984 = A035490(A057983).

A060751 These numbers take a record number of steps to reach the top of the deck in Guy's shuffle (see A060750).

Original entry on oeis.org

1, 4, 7, 13, 15, 39, 43, 54, 1227, 1796, 2674, 3464, 6057, 7650, 17083
Offset: 0

Views

Author

Jud McCranie, Oct 24 2000

Keywords

Comments

See A060752 for the number of steps for these to reach the top of the deck.

References

  • See A057983 for references, links and programs.

Crossrefs

Cf. A035485, A035490, A035493, A035494, A057984, A060750, A060752.

A060752 These numbers are the record number of steps for the numbers in A060751 to reach the top of the deck in Guy's shuffle (see A060750).

Original entry on oeis.org

3, 8, 78, 349, 383, 13932, 30452, 252992198, 364873753, 850627701, 914514429, 17493745212, 471008431072, 1027221839335, 14568535208344
Offset: 0

Views

Author

Jud McCranie, Oct 24 2000

Keywords

References

  • See A057984 for references, links and programs.

Crossrefs

Cf. A035485, A035490, A035493, A035494, A057983, A060750, A060751.

A035500 Shuffles at which new cards appear on top of deck in Guy's shuffling problem A035485.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 25, 26, 28, 29, 30, 32, 33, 35, 37, 38, 39, 40, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 60, 62, 64, 65, 66, 72, 73, 76, 77, 78, 83, 84, 85, 86, 87, 88, 89, 90, 91, 94, 95, 97, 98, 99, 101, 102, 103, 104
Offset: 1

Views

Author

N. J. A. Sloane, Wouter Meeussen

Keywords

References

  • D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," 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

Crossrefs

Cf. A035485, A035493, A035501.

Programs

  • Python
    from itertools import count, islice
def agen(): # generator of terms
    deck = []; tops = {1}; yield 0
    for n in count(1):
        deck += [2*n-1, 2*n]
        first, next = deck[:n], deck[n:2*n]
        deck[0:2*n:2], deck[1:2*n:2] = next, first
        if deck[0] not in tops: tops.add(deck[0]); yield n
print(list(islice(agen(), 70))) # Michael S. Branicky, Aug 11 2022

Extensions

Extended (and corrected) by Jud McCranie

A035501 Shuffles at which new record high cards appear on top of deck in Guy's shuffling problem A035485.

Original entry on oeis.org

0, 1, 2, 4, 6, 10, 14, 19, 20, 21, 22, 30, 46, 52, 62, 72, 76, 85, 94, 120, 126, 144, 147, 169, 174, 190, 216, 221, 241, 251, 254, 273, 281, 289, 292, 300, 301, 305, 308, 323, 338, 341, 379, 382, 399, 421, 429, 447, 448, 449, 473, 479, 490, 509, 510, 544, 561, 583, 588, 615, 632, 651, 686, 715, 726, 764
Offset: 1

Views

Author

N. J. A. Sloane, Wouter Meeussen

Keywords

References

  • D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," 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.

Crossrefs

Cf. A035485, A035493, A035494, A035501.

Programs

  • Python
    from itertools import count, islice
def agen(): # generator of terms
    deck = []; record = 1; yield 0
    for n in count(1):
        deck += [2*n-1, 2*n]
        first, next = deck[:n], deck[n:2*n]
        deck[0:2*n:2], deck[1:2*n:2] = next, first
        if deck[0] > record: record = deck[0]; yield n
print(list(islice(agen(), 66))) # Michael S. Branicky, Aug 11 2022

Extensions

More terms from Jud McCranie
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.