1,1

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.

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 Erdos is Eighty. Bolyai Society Math. Studies, Vol. 1, pp. 193-206, 1993.

R. K. Guy and R. J. Nowakowski, ``Mousetrap,'' Amer. Math. Monthly, 101 (1994), 1007-1010.

A. M. Bersani, On the game Mousetrap.

a(4)=2 since 4213->2134->3214, 1432->1423->1234 are the only two permutations that can be reformed twice.

Cf. A007709, A007711, A007712, A067950.

Sequence in context: A038586 A140316 A088587 this_sequence A080958 A138351 A120293

Adjacent sequences: A055456 A055457 A055458 this_sequence A055460 A055461 A055462

nonn

Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 05 2000

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