|
|
A032435
|
|
Triangle of second-to-last man to survive in Josephus problem of n men in a circle with every k-th killed, with 1 <= k <= n and n >= 2.
|
|
3
|
|
|
1, 1, 2, 1, 1, 3, 1, 1, 2, 4, 3, 2, 1, 2, 5, 1, 1, 5, 1, 4, 6, 3, 1, 2, 1, 3, 4, 7, 1, 4, 6, 3, 1, 3, 4, 8, 3, 1, 1, 2, 7, 1, 3, 7, 9, 5, 4, 5, 3, 3, 8, 1, 6, 4, 10, 7, 2, 9, 1, 9, 4, 1, 4, 3, 4, 11, 1, 5, 1, 1, 3, 11, 5, 1, 1, 3, 2, 12, 3, 8, 5, 6, 9, 5, 4, 10, 2, 1, 1, 7, 13, 5, 2, 9, 2, 1, 12, 7, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,3
|
|
REFERENCES
|
W. W. R. Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover, pp. 32-36, 1987.
M. Kraitchik, "Josephus' Problem", Sec. 3.13 in Mathematical Recreations, New York: W. W. Norton, pp. 93-94, 1942.
Eric W. Weisstein, The CRC Concise Encyclopedia in Mathematics, 2nd ed., Chapman and Hall/CRC, 2002. [The first 8 rows of the triangle appear on p. 1595 of this book under the topic "Josephus Problem".]
|
|
LINKS
|
F. Jakóbczyk, On the generalized Josephus problem, Glasow Math. J. 14(2) (1973), 168-173. [It contains algorithms that allow the identification of the original position of the second-to-last person to survive in Josephus problem.]
Eric Weisstein's World of Mathematics, Josephus Problem. [It contains a new, apparently corrected, triangle.]
|
|
EXAMPLE
|
Triangle T(n,k) (with rows n >= 2 and columns k = 2..n) begins
1, 1;
2, 1, 1;
3, 1, 1, 2;
4, 3, 2, 1, 2;
5, 1, 1, 5, 1, 4;
6, 3, 1, 2, 1, 3, 4;
7, 1, 4, 6, 3, 1, 3, 4;
8, 3, 1, 1, 2, 7, 1, 3, 7;
9, 5, 4, 5, 3, 3, 8, 1, 6, 4;
10, 7, 2, 9, 1, 9, 4, 1, 4, 3, 4;
11, 1, 5, 1, 1, 3, 11, 5, 1, 1, 3, 2;
...
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|