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
Keywords
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
Programs
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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:
Comments