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

Author

Paul Weisenhorn, Jan 06 2013

Keywords

• nonn

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.

Examples

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

References

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

Links

• 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

Crossrefs

Cf. A187789, A206602.

First column in A321781.

Programs

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: