A163789 a(n) is the n-th J_9-prime (Josephus_9 prime).

3, 39, 53, 2347, 6271, 121105, 386549, 519567, 958497

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 9th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_9-prime if this permutation consists of a single cycle of length N.

There are 9 J_9-primes in the interval 2..1000000 only. No formula is known; the J_9-primes have been 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..9.

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

All J_9-primes are odd.

Crossrefs

CF. A163782 through A163788 for J_2- through J_8-primes.

Cf. A163790 through A163800 for J_10- through J_20-primes.

Sequence in context: A213003 A213004 A359081 * A183182 A277713 A134106

Adjacent sequences: A163786 A163787 A163788 * A163790 A163791 A163792

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 05 2009

Status

approved