A094679
n sets a new record for number of iterations to reach 1 in the juggler sequence problem.
Original entry on oeis.org
1, 2, 3, 9, 19, 25, 37, 77, 163, 193, 1119, 1155, 4065, 4229, 4649, 7847, 13325, 34175, 59739, 78901, 636731, 1122603, 1301535, 2263913, 5947165, 72511173, 78641579, 125121851, 198424189, 4488817391
Offset: 1
78901 takes 258 iterations to reach 1; see A094698 for the others.
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$MaxPrecision = 250000000; js[n_] := If[ EvenQ[ n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Block[{c = 1, k = n}, While[k = js[k]; k != 1, c++ ]; c]; a = {0}; Do[ b = f[n]; If[b > a[[ -1]], AppendTo[a, b]], {n, 3053595}]; a (* Robert G. Wilson v *)
A094698
Number of steps where the Juggler sequence reaches a new record.
Original entry on oeis.org
0, 1, 6, 7, 9, 11, 17, 19, 43, 73, 75, 80, 88, 96, 107, 131, 166, 193, 201, 258, 263, 268, 271, 298, 335, 340, 443, 479, 484, 527
Offset: 1
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$MaxPrecision = 250000000; js[n_] := If[ EvenQ[ n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Block[{c = 1, k = n}, While[k = js[k]; k != 1, c++ ]; c]; a = {0}; Do[ b = f[n]; If[b > a[[ -1]], AppendTo[a, b]; Print[n]], {n, 3053595}] (* Robert G. Wilson v, Jun 14 2004 *)
A143745
The next largest juggler number.
Original entry on oeis.org
1, 2, 36, 140, 52214, 24906114455136, 202924588924125339424550328
Offset: 1
24906114455136 is in the sequence because starting at 37 the juggler sequences maxes out at 24906114455136, a 14-digit number, after 8 steps. This is the largest juggler number found for starting values less than or equal to 37.
- C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.
A143742
Starting values that produce a larger juggler number than smaller starting values.
Original entry on oeis.org
1, 2, 3, 9, 25, 37, 113, 173, 193, 2183, 11229, 15065, 15845, 30817, 48443, 275485, 1267909, 2264915, 5812827, 7110201
Offset: 1
37 is in the sequence because starting at 37 the juggler sequences maxes out at 24906114455136, a 14-digit number, after 8 steps. This is the largest juggler number found for starting values less than or equal to 37.
- C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.
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DeleteDuplicates[Table[{n,Max[NestWhileList[If[EvenQ[#],Floor[Sqrt[#]],Floor[Sqrt[#^3]]]&,n,#!=1&]]},{n,50000}],GreaterEqual [#1[[2]],#2[[2]]]&][[;;,1]] (* The program generates the first 15 terms of the sequence. *) (* Harvey P. Dale, Dec 21 2024 *)
A143743
The number of digits in the next largest juggler number.
Original entry on oeis.org
1, 1, 2, 3, 5, 14, 27, 82, 271, 5929, 8201, 11723, 23889, 45391, 972463, 1909410, 1952329, 2855584, 7996276
Offset: 1
14 is in the sequence because starting at 37 the juggler sequence maxes out at 24906114455136, a 14-digit number, after 8 steps. This is the largest juggler number found for starting values less than or equal to 37.
- C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.
A143744
The number of steps needed to generate the next largest juggler number.
Original entry on oeis.org
0, 0, 3, 2, 3, 8, 9, 17, 47, 32, 54, 25, 43, 39, 60, 148, 99, 89, 67
Offset: 1
8 is in the sequence because starting at 37 the juggler sequences maxes out at 24906114455136, a 14-digit number, after 8 steps. This is the largest juggler number found for starting values less than or equal to 37.
- C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.
A284987
Juggler sequence starting at 37.
Original entry on oeis.org
37, 225, 3375, 196069, 86818724, 9317, 899319, 852846071, 24906114455136, 4990602, 2233, 105519, 34276462, 5854, 76, 8, 2, 1
Offset: 0
- David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, 1997, page 99.
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Juggler(n)={my(L=List([n])); while(n<>1, n=sqrtint(n^(2-(-1)^n)); listput(L,n)); Vec(L)}
{ Juggler(37) } \\ Andrew Howroyd, Apr 27 2020
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