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 1-4 of 4 results.

A095908 Duplicate of A094698.

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
Offset: 1

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Keywords

A007320 Number of steps needed for juggler sequence (A094683) started at n to reach 1.

Original entry on oeis.org

0, 1, 6, 2, 5, 2, 4, 2, 7, 7, 4, 7, 4, 7, 6, 3, 4, 3, 9, 3, 9, 3, 9, 3, 11, 6, 6, 6, 9, 6, 6, 6, 8, 6, 8, 3, 17, 3, 14, 3, 5, 3, 6, 3, 6, 3, 6, 3, 11, 5, 11, 5, 11, 5, 11, 5, 5, 5, 11, 5, 11, 5, 5, 3, 5, 3, 11, 3, 14, 3, 5, 3, 8, 3, 8, 3, 19, 3, 8, 3, 10, 8, 8, 8, 11, 8, 10, 8, 11, 8, 11, 8, 11, 8, 8, 8, 11
Offset: 1

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Keywords

Comments

It is not known if every starting value eventually reaches 1.

Examples

			The trajectory of 1 is 3, 5, 11, 36, 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... so a(3) = 6.
		

References

  • C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 232.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Programs

  • Maple
    A007320 := proc(n)
        local a,ntrack;
        a := 0 ;
        ntrack := n ;
        while ntrack > 1 do
            ntrack := A094683(ntrack) ;
            a := a+1 ;
        end do:
        return a;
    end proc: # R. J. Mathar, Apr 19 2013
  • Mathematica
    js[n_] := If[ EvenQ[n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Length[ NestWhileList[js, n, # != 1 &]] - 1; Table[ f[n], {n, 99}] (* Robert G. Wilson v, Jun 10 2004 *)

Extensions

Corrected and extended by Jason Earls, Jun 09 2004

A094670 Smallest number which requires n iterations to reach 1 in the juggler sequence problem.

Original entry on oeis.org

1, 2, 4, 16, 7, 5, 3, 9, 33, 19, 81, 25, 353, 183, 39, 201, 103, 37, 205, 77, 681, 263, 3817, 429, 175, 1673, 539, 165, 671, 321, 5875, 477, 173, 2243, 265, 29017, 1011, 677, 9361, 659, 241, 3389, 1123, 163, 2057, 625, 15271, 4481
Offset: 0

Views

Author

Jason Earls, Jun 09 2004

Keywords

Comments

A juggler sequence is defined as follows: given a positive integer x, repeat: if x is even then x <- [x^(1/2)] else x <- [x^(3/2)] until x=1. The brackets indicate the floor function.
a(104) is unknown ( > 10000000). - Robert G. Wilson v, Jun 11 2014

Crossrefs

Programs

  • Mathematica
    js[n_] := If[ EvenQ[ n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Length[ NestWhileList[js, n, # != 1 &]] - 1; a = Table[0, {50}]; Do[ b = f[n]; If[b < 51 && a[[b]] == 0, a[[b]] = n; Print[n, " = ", b]], {n, 10^5}] (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v, Jun 14 2004

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

Views

Author

Jason Earls, Jun 09 2004

Keywords

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, Jun 14 2004
78901 reaches a maximum of 4064983429...(skip the next 371727 digits)...2140697134 during its trip to 1. - Robert G. Wilson v, Jun 14 2004
I postulate that 2 is the only even number in this sequence. - Harry J. Smith, Aug 15 2008
a(30) > 1.6*10^9. - Giovanni Resta, Apr 08 2017

Examples

			78901 takes 258 iterations to reach 1; see A094698 for the others.
		

Crossrefs

Programs

  • 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 (* Robert G. Wilson v *)

Extensions

More terms from Robert G. Wilson v, Jun 14 2004
a(25) = 5947165 from Eric W. Weisstein, Jan 25 2006
a(26)-a(27) from Robert G. Wilson v, Jun 15 2014
a(28)-a(29) from Giovanni Resta, Apr 08 2017
a(30) from Ethan Slota, Apr 15 2025
Showing 1-4 of 4 results.