A163799 a(n) is the n-th J_19-prime (Josephus_19 prime).

15, 145, 149, 243, 259, 449, 1921, 2787, 15871, 18563, 26459, 191515, 283269, 741343, 844805

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 19th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_19-prime if this permutation consists of a single cycle of length N.

There are 15 J_19-primes in the interval 2..1000000 only. No formula is known; the J_19-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..15.

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_19-primes are odd.

Crossrefs

Cf. A163762 through A163798 and A163800 for J_2- through J_18- and J_20-primes.

Sequence in context: A270511 A026893 A368075 * A206810 A025440 A155638

Adjacent sequences: A163796 A163797 A163798 * A163800 A163801 A163802

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 04 2009

Status

approved