OFFSET
1,1
COMMENTS
Consider a permutation {a1,...,an}; start counting from the beginning: if a1 is not 1, a1 is replaced at the end of an, until we reach the first i such that ai=i in which case ai is removed and the count start from 1 again. The permutation is unreformable if a count of n+1 is reached before all ai are removed. Otherwise, the order of removal of the ai defines the reformed permutation.
REFERENCES
A. M. Bersani, "Reformed permutations in Mousetrap and its generalizations", preprint MeMoMat n. 15/2005.
R. K. Guy and R. J. Nowakowski, "Mousetrap," in D. Miklos, V. T. Sos and T. Szonyi, eds., Combinatorics, Paul Erdős is Eighty. Bolyai Society Math. Studies, Vol. 1, pp. 193-206, 1993.
LINKS
A. M. Bersani, On the game Mousetrap.
R. K. Guy and R. J. Nowakowski, Mousetrap Amer. Math. Monthly, 101 (1994), 1007-1010.
EXAMPLE
a(4)=2 since 4213->2134->3214, 1432->1423->1234 are the only two permutations that can be reformed twice.
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jul 05 2000
EXTENSIONS
Edited by Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Mar 06 2002
2 more terms from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 07 2007
One more term from Alberto M. Bersani (bersani(AT)dmmm.uniroma1.it), Feb 24 2008
STATUS
approved