A163797 a(n) is the n-th J_17-prime (Josephus_17 prime).

3, 5, 7, 39, 93, 267, 557, 2389, 2467, 4059, 4681, 6213, 70507, 151013, 282477, 421135

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 17th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_17-prime if this permutation consists of a single cycle of length N.

There are 16 J_17-primes in the interval 2..1000000 only. No formula is known; the J_17-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..16.

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_17-primes are odd.

Crossrefs

Cf. A163782 through A163796 for J_2- through J_16-primes.

Cf. A163798 through A163800 for J_18- through J_20-primes.

Sequence in context: A087363 A234569 A037287 * A339900 A130536 A261511

Adjacent sequences: A163794 A163795 A163796 * A163798 A163799 A163800

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 04 2009

Status

approved