A163795 a(n) is the n-th J_15-prime (Josephus_15 prime).

3, 9, 13, 25, 49, 361, 961, 1007, 2029, 8593, 24361, 44795, 88713

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 15th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_15-prime if this permutation consists of a single cycle of length N.

There are 13 J_15-primes in the interval 2..1000000 only. No formula is known; the J_15-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..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

All J_15-primes are odd.

Crossrefs

Cf. A163782 through A163794 for J_2- through J_14-primes.

Cf. A163796 through A163800 for J_16- through J_20-primes.

Sequence in context: A106402 A125706 A113510 * A079994 A303964 A124825

Adjacent sequences: A163792 A163793 A163794 * A163796 A163797 A163798

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 04 2009

Status

approved