A163791 a(n) is the n-th J_11-prime (Josephus_11 prime).

3, 9, 27, 47, 63, 185, 617, 15189, 56411, 182439, 271607, 658521

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 11th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_11-prime if this permutation consists of a single cycle of length N.

There are 12 J_11-primes in the interval 2..1000000 only. No formula is known; the J_11-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..12.

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_11-primes are odd.

Crossrefs

Cf. A163782 through A163790 for J_2- through J_10-primes.

Cf. A163792 through A163800 for J_12- through J_20-primes.

Sequence in context: A056024 A116475 A337948 * A248078 A057829 A181047

Adjacent sequences: A163788 A163789 A163790 * A163792 A163793 A163794

Keyword

nonn,more,changed

Author

Peter R. J. Asveld, Aug 04 2009

Status

approved