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 1-5 of 5 results.

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.

A035490 Step at which card n appears on top of deck for first time in Guy's shuffling problem A035485.

Original entry on oeis.org

0, 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

Wouter Meeussen

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 accept 0 as a valid number of shuffles and so we say that card #1 first shows up on top after 0 shuffles (i.e., initially). A057983 and A057984 also adopt this convention. Alternatively, we can say that card #1 first shows up on top after 3 shuffles; this leads to sequences A060750, A060751, A060752.

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, A035491-A035494, A060750-A060752.

Programs

  • Mathematica
    riguy[ deck_List ] := Module[ {le=Length[ deck ]}, Flatten[ Transpose[ Reverse@ Partition[ Flatten[ {deck, le+1, le+2 } ], le/2+1 ] ] ] ]
Table[ Length[ FixedPoint[ riguy, {}, SameTest->(#2[ [ 1 ] ]=== i &) ] ]/2, {i, 2, 38} ]
  • UBASIC
    10 input N; 20 clr time; 30 I=(N-1)\2; 40 while N>1; 50 inc I; 60 if N>I then N=2*(N-I)-1 else N+=N; 70 wend; 80 print I; time; 90 goto 10;

Extensions

Thanks to Colin Mallows, David W. Wilson, Wouter Meeussen and others for helping fill 3 lines - N. J. A. Sloane.
Additional comments from David W. Wilson, Apr 22 2001

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

A081058 Number of shuffles in Guy's shuffle (see A035485) for the card that is at the top of the deck after n shuffles to come to the top again.

Original entry on oeis.org

8, 263, 4, 23, 370, 790, 43, 48, 218, 5, 12, 22, 11, 29, 53, 26, 231, 583, 90, 271, 1988, 14, 52, 17, 6, 286, 31, 39, 40, 15, 320158, 354, 812, 487, 118, 43, 758, 470, 78, 689, 39, 29, 18, 12552564, 70, 249, 53, 2054, 10, 43, 409, 309, 13519, 224, 26, 7, 35, 800
Offset: 1

Views

Author

Jud McCranie, Mar 04 2003

Keywords

Comments

Corresponding shuffle number is in A081059. A081059[n]=A081058[n]+n.

Examples

			After 2 shuffles, card #3 is on top. It reaches the top again on shuffle # 265 (263 shuffles later), so a(2)=263.

Crossrefs

Cf. A035485, A060750, A060751, A081059.

A081059 Shuffle number in Guy's shuffle (see A035485) for the card that is at the top of the deck after n shuffles to come to the top again.

Original entry on oeis.org

9, 265, 7, 27, 375, 796, 50, 56, 227, 15, 23, 34, 24, 43, 68, 42, 248, 601, 109, 291, 2009, 36, 75, 41, 31, 312, 58, 67, 69, 45, 320189, 386, 845, 521, 153, 79, 795, 508, 117, 729, 80, 71, 61, 12552608, 115, 295, 100, 2102, 59, 93, 460, 361, 13572, 278, 81
Offset: 1

Views

Author

Jud McCranie, Mar 04 2003

Keywords

Comments

Number of shuffles later is in A081058. A081059[n]=A081058[n]+n.

Examples

			After 2 shuffles, card #3 is on top. It reaches the top again on shuffle # 265, so a(2)=265.

Crossrefs

Cf. A035485, A060750, A060751, A081058.
Showing 1-5 of 5 results.

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

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