A163787 a(n) is the n-th J_7-prime (Josephus_7 prime).

5, 11, 21, 35, 85, 103, 161, 231, 543, 1697, 1995, 2289, 37851, 49923, 113443, 236091, 285265

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 7th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_7-prime if this permutation consists of a single cycle of length N.

There are 17 J_7-primes in the interval 2..1000000 only. No formula is known; the J_7-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..17.

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_7-primes are odd.

Crossrefs

Cf. A163782 through A163786 for J_2- through J_6-primes.

Cf. A163788 through A163800 for J_8- through J_20-primes.

Sequence in context: A166480 A164096 A298785 * A166863 A163704 A131898

Adjacent sequences: A163784 A163785 A163786 * A163788 A163789 A163790

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 05 2009

Status

approved