A163790 a(n) is the n-th J_10-prime (Josephus_10 prime).

2, 17, 98, 174, 181, 238, 6774, 9057, 44929, 54594, 58389

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 10th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_10-prime if this permutation consists of a single cycle of length N.

There are 11 J_10-primes in the interval 2..1000000 only. No formula is known; the J_10-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..11.

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_10-prime (trivial).

Crossrefs

Cf. A163782 through A163789 for J_2- through J_9-primes.

Cf. A163791 through A163800 for J_11- through J_20-primes.

Sequence in context: A358591 A002645 A100268 * A129123 A109724 A127533

Adjacent sequences: A163787 A163788 A163789 * A163791 A163792 A163793

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 05 2009

Status

approved