A163788 a(n) is the n-th J_8-prime (Josephus_8 prime).

2, 6, 10, 62, 321, 350, 686, 3217, 4981, 21785, 22305, 350878, 378446, 500241, 576033, 659057, 917342

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 8th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_8-prime if this permutation consists of a single cycle of length N.

There are 17 J_8-primes in the interval 2..1000000 only. No formula is known; the J_8-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..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

2 is a J_8-prime (trivial).

Crossrefs

Cf. A163782 through A163787 for J_2- through J_7-primes.

Cf. A163789 through A163800 for J_9- through J_20-primes.

Sequence in context: A222559 A095107 A115113 * A361792 A324547 A093880

Adjacent sequences: A163785 A163786 A163787 * A163789 A163790 A163791

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 05 2009

Status

approved