

A178853


"Josephus problem": n persons stand in a circle and eliminate every seventh person counting clockwise until only person a(n) is remaining.


2



1, 2, 3, 2, 4, 5, 5, 4, 2, 9, 5, 12, 6, 13, 5, 12, 2, 9, 16, 3, 10, 17, 1, 8, 15, 22, 2, 9, 16, 23, 30, 5, 12, 19, 26, 33, 3, 10, 17, 24, 31, 38, 2, 9, 16, 23, 30, 37, 44, 1, 8, 15, 22, 29, 36, 43, 50, 57, 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 76
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OFFSET

1,2


REFERENCES

L. Euler, Observationes circa novum et singulare progressionum genus. In: Novi Comment. Akadem. Petropol. Vol.20 (1775) [From Roland Schroeder (florola(AT)gmx.de), Jul 13 2010]


LINKS

Table of n, a(n) for n=1..79.
Eric Weisstein's World of Mathematics, Josephus Problem. [From Robert G. Wilson v, Jul 31 2010]
Index entries for sequences related to the Josephus Problem


MATHEMATICA

(* First do *) Needs["Combinatorica`"] (* then *) f[n_] := Last@ InversePermutation@ Josephus[n, 7]; Array[f, 79] (* Robert G. Wilson v, Jul 31 2010 *)


PROG

(Other) DERIVE  program R(x) := VECTOR(y, y, 1, x) g(v, k) := VECTOR(ELEMENT(v, n), n, 1, IF(k = DIMENSION(v), DIMENSION(v)  1, MOD(k, DIMENSION(v)))) f(v, k) := VECTOR(ELEMENT(v, n), n, IF(k = DIMENSION(v), DIMENSION(v) + 1, MOD(k, DIMENSION(v)) + 1), DIMENSION(v)) H(v, k) := APPEND(f(v, k), g(v, k)) i(v, k) := DELETE_ELEMENT(H(v, k), DIMENSION(v)) j(v, k) := ITERATES(i(w, k), w, v, DIMENSION(v)  1) jo(x, k) := ITERATE(i(w, k), w, R(x), x  1) VECTOR((jo(x, 7))sub1, x, 1, 100)


CROSSREFS

Sequence in context: A090321 A241255 A174625 * A120641 A008666 A240854
Adjacent sequences: A178850 A178851 A178852 * A178854 A178855 A178856


KEYWORD

nonn


AUTHOR

Roland Schroeder (florola(AT)gmx.de), Jun 18 2010


EXTENSIONS

Several other versions of this sequence are already in the OEIS.  N. J. A. Sloane, Jun 24 2010
a(29) onwards from Robert G. Wilson v, Jul 31 2010


STATUS

approved



