What is a Juggler Number?




  Juggler Sequence defined in Dr. Clifford A. Pickover's book "Computers and
  the Imagination." This book has scores of educational and recreational
  experiments that can be done on a personal computer.

  At the end of Appendix C in this book you will find:

  ". . . An award of 50 dollars is offered by the publisher for a printout of
  the largest Juggler number computed by readers. . . . Currently the largest
  juggler number computed s a 45,391-digit giant from the starting number
  30817. It was computed by Harry J. Smith using hid own software package to
  perform multiple precision integer arithmetic. His package is written in the
  object-oriented programming language Turbo Pascal 5.5 by Borland
  International, Inc. His juggler package is a subset of his super-precision
  calculator software which computes transcendental functions to thousand of
  decimal places. Write him to obtain the software: . . ."

  Juggler Sequence also defined in Nov 1990 issue of Algorithm in PERSONAL
  PROGRAMS by Clifford A. Pickover.

  Pickover's definition of a juggler sequence:

  input positive integer, x
  repeat
    if x is even
      then x <-- [x^(1/2)]
      else x <-- [x^(3/2)]
  until x=1

  The bracket signs indicate that non-integer numbers are truncated
  (i.e., 4.9 -> 4).

  A Juggler number is any number in a Juggler sequence.

  The Juggler Sequence starting with x(0) = 48443 has a max juggler number at
  x(60), a 972,463-digit number.

Summary output of program JugglerC
-----------------------------------
x(0) max with 1 digits for x(0) = 1
x(0) max with 1 digits for x(0) = 2
x(3) max with 2 digits for x(0) = 3
x(2) max with 3 digits for x(0) = 9
x(3) max with 5 digits for x(0) = 25
x(8) max with 14 digits for x(0) = 37
x(9) max with 27 digits for x(0) = 113
x(17) max with 82 digits for x(0) = 173
x(47) max with 271 digits for x(0) = 193
x(32) max with 5929 digits for x(0) = 2183
x(54) max with 8201 digits for x(0) = 11229
x(25) max with 11723 digits for x(0) = 15065
x(43) max with 23889 digits for x(0) = 15845
x(39) max with 45391 digits for x(0) = 30817
x(60) max with 972463 digits for x(0) = 48443
x(148) max with 1909410 digits for x(0) = 2,75485
x(99) max with 1952329 digits for x(0) = 12,67909
x(89) max with 2855584 digits for x(0) = 22,64915
x(67) max with 7996276 digits for x(0) = 58,12827
x(90) max with 41564193 digits for x(0) = 71,10201  not final

x(115) max with 53322381 digits for x(0) = 71,10201 not final, this gave
U  Up started  Numbers too large for FHT multiply, digits =
71096512 > 2^26 = 67,108,864

PARI gave
x(119) max with 89981517 digits for x(0) = 7110201 not final, this gave
  *** if: length (lg) overflow

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This page accessed times since October 20, 2004.
Page created by: hjsmithh@sbcglobal.net
Changes last made on Friday, 27-Mar-09 07:17:28 PDT

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