A163792 a(n) is the n-th J_12-prime (Josephus_12 prime).

2, 38, 57, 145, 189, 2293, 2898, 6222, 7486, 26793, 45350, 90822, 177773

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 12th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_12-prime if this permutation consists of a single cycle of length N.

There are 13 J_12-primes in the interval 2..1000000 only. No formula is known; the J_12-primes were found by exhaustive search.

References

R. L. Graham, D. E. Knuth & O. Patashnik, Concrete Mathematics (1989), Addison-Wesley, Reading, MA. Sections 1.3 & 3.3.

Links

Table of n, a(n) for n=1..13.

P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.

P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology, 2014. University link.

Index entries for sequences related to the Josephus Problem

Example

2 is a J_12-prime (trivial).

Crossrefs

Cf. A163782 through A163791 for J_2- through J_11-primes.

Cf. A163793 through A163800 for J_13- through J_20-primes.

Sequence in context: A284309 A227468 A049487 * A050899 A068401 A173026

Adjacent sequences: A163789 A163790 A163791 * A163793 A163794 A163795

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 04 2009

Status

approved