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A094679
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n sets a new record for number of iterations to reach 1 in the juggler sequence problem.
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Where records occur in A007320.
The Juggler sequence: begin with x and if x is even, [sqrt(x)] -> x and if x is odd, [sqrt(x^3)] -> x and repeat until x = 1, count the iterations. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 14 2004
78901 reaches a maximum of 4064983429...(skip the next 371727 digits)...2140697134 during its trip to 1. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 14 2004
I postulate that 2 is the only even number in this sequence. - Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 15 2008
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LINKS
| Eric Weisstein's World of Mathematics, Juggler Sequence
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EXAMPLE
| 78901 takes 258 iterations to reach 1; see A094698 for the others.
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MATHEMATICA
| $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 (from Robert G. Wilson v)
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CROSSREFS
| Cf. A007320, A094670, A094698, A095906, A094698.
Sequence in context: A108827 A113201 A089753 * A094812 A079992 A106519
Adjacent sequences: A094676 A094677 A094678 * A094680 A094681 A094682
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KEYWORD
| more,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jun 09 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 14 2004
a(25) = 5947165 from Eric Weisstein (eric(AT)weisstein.com), Jan 25, 2006
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