A006852 Step at which n is expelled in Kimberling's puzzle (A035486). (Formerly M5181)

1, 25, 2, 4, 3, 22, 6, 8, 10, 5, 32, 83, 44, 14, 7, 66, 169, 11, 49595, 9, 69, 16, 24, 12, 43, 47, 7598, 15, 133, 109, 13, 198, 19, 33, 18, 23, 58, 65, 60, 93167, 68, 17, 1523, 39, 75, 20, 99, 34, 117, 123

Offset

1,2

References

R. K. Guy, Unsolved Problems Number Theory, Sect E35.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Enrique Pérez Herrero [1..11000], Goudout Élie [11001..20000], Table of n, a(n) for n = 1..20000

D. Gale, Tracking the Automatic Ant: And Other Mathematical Explorations, ch. 5, p. 27. Springer, 1998. [From Enrique Pérez Herrero, Mar 28 2010]

C. Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991.

Formula

a(n) >= floor((n+4)/3), n is expulsed from the unshuffled zone. - Enrique Pérez Herrero, Feb 25 2010

Mathematica

L[n_] := L[n] = (
i = Floor[(n + 4)/3];
j = Floor[(2*n + 1)/3];
While[(i != j), j = Max[2*(i - j), 2*(j - i) - 1]; i++ ];
Return[i];
) A006852[n_] := L[n]
(* Enrique Pérez Herrero, Mar 28 2010 *)

Prog

(PARI) A006852(n)=
{
my(i, j);
i=floor((n+4)/3);
j=floor((2*n+1)/3);
while((i!=j),
j=max(2*i-2*j, -1-2*i+2*j);
i++;
); return(i); }
\\ Enrique Pérez Herrero, Feb 25 2010

Crossrefs

Cf. A007063.

Cf. A175312. - Enrique Pérez Herrero, Mar 28 2010

Sequence in context: A040616 A040620 A040621 * A040622 A040623 A317470

Adjacent sequences: A006849 A006850 A006851 * A006853 A006854 A006855

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

7593 corrected to 7598 by Hans Havermann, July 1998

Status

approved