A187788 a(n) is the least step for the Sankt-Petrus-game with n white and n black stones.

2, 5, 2, 4, 3, 11, 2, 3, 8, 16, 4, 21, 6, 5, 2, 11, 20, 34, 8, 15, 10, 7, 13, 11, 13, 45, 18, 23, 8, 3, 2, 25, 75, 42, 13, 5, 23, 13, 50, 16, 18, 89, 38, 8, 39, 30, 29, 38, 7, 45, 23, 137, 46, 63, 17, 48, 5, 46, 34, 140, 33, 39, 2, 28, 29, 79, 33, 48, 3, 10, 46, 120, 6, 37, 17, 8, 44, 15, 160, 20, 35, 144, 104, 179, 153, 24, 8, 265, 19, 9, 62, 7, 139, 19, 44, 93, 182, 27, 158, 185

Offset

1,1

Comments

Beginning at the position A187789(n) with step a(n), (n-1) white stones were eliminated; then from the position 1 of the last white stone, n black stones were eliminated.

References

W. Ahrens, Das Josephusspiel, Archiv für Kulturgeschichte, Jg 11(1913), 129-151.

Links

Table of n, a(n) for n=1..100.

R. Baumann, Das Josephus-Problem, LOG IN, Heft Nr. 165, pp. 68-71, 2010 (in German).

Index entries for sequences related to the Josephus Problem

Example

n=4; WBWWBBWB; startposition=A187789(4)=8; least step=a(4)=4; elimination: white stones: {3,7,4}; black stones: {6,5,8,2}.

Maple

s:=1: M:={}:
for n from 1 to 100 do M:=M union {n}:
while (M <> {}) do
  s1:=s: s:=s+1: f[1]:=1:
  for n from 2 to 101 do  n1:=n-1:
    f[n]:=(f[n1]+s1) mod n +1:
    if (f[n]=1) and (n1 in M) then
      a[n1]:=s: M:=M minus {n1}:
    end if:
  end do:
end do:

Crossrefs

Cf. A187789, A206602.

First column in A321781.

Sequence in context: A197207 A197805 A334754 * A085072 A077200 A275748

Adjacent sequences: A187785 A187786 A187787 * A187789 A187790 A187791

Keyword

nonn

Author

Paul Weisenhorn, Jan 06 2013

Status

approved