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

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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.

Crossrefs

Cf. A007063.

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

Programs

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 *)

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

Formula

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

Extensions

7593 corrected to 7598 by Hans Havermann, July 1998