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A206602 a(n) is the number of white and black stones lying in a circle; starting with place 1, the first a(n) steps of length 5 give the places of white stones. Beginning with last place, the next a(n) steps give the places of black stones. 2
2, 5, 11, 14, 36, 57, 141, 221, 346, 677, 4042, 9870, 114916, 179557, 1070250, 2612917, 9967491, 12459364, 19467757, 30418371, 38022964, 59410882, 116036880, 283293166, 553306966, 864542135, 1080677669, 3297966522, 8051676081, 15725929847, 19657412309, 47991729272 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The game eliminates (a(n)-1) white and a(n) black stones; the a(n)-th white stone survives. The game is known under different names; e.g. "Sankt Peters Spiel" or "Ludus Sancti Petri" or "Josephus problem".

It gives sequences for every step length s from 2.

s=2: a(n)=2^n-1;

s=3: 3,5,8,30,69,104,354,798,1797,2696,9102,20481.

REFERENCES

R. Baumann, Computer Knobelei, LOG IN, 165(2010), 68-71.

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

The solution for a(3) = 11: (WBWBWBWBWWBBBWWWBBBWBW);

White stones: (5,10,15,20,3,9,16,22,7,14,1);

Black stones: (8,18,4,17,6,21,13,12,20,2,11).

MAPLE

s:=5: s1:=s-1: a:=1:

for p from 2 to 100000 by 2 do

  b:=(a+s1) mod p +1:

  if (b=1) then printf("%9d", p-1): end if:

  a:=(b+s1) mod (p+1) +1:

if (a=1) then printf("%9d", p): end if:

end do:

CROSSREFS

Sequence in context: A287708 A026228 A003420 * A238159 A080156 A082083

Adjacent sequences:  A206599 A206600 A206601 * A206603 A206604 A206605

KEYWORD

nonn

AUTHOR

Paul Weisenhorn, Feb 10 2012

STATUS

approved

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Last modified January 29 11:16 EST 2020. Contains 331337 sequences. (Running on oeis4.)