A163798 a(n) is the n-th J_18-prime (Josephus_18 prime).

2, 5, 462, 530, 6021, 14686, 19537, 67161, 1766014, 1921621, 2779501

Offset: 1

Author

Peter R. J. Asveld, Aug 04 2009

Keywords

• nonn
• more

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 18th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_18-prime if this permutation consists of a single cycle of length N.

There are 8 J_18-primes in the interval 2..1000000 only. No formula is known; the J_18-primes were found by exhaustive search.

Examples

			2 is a J_18-prime (trivial).
		

References

• R. L. Graham, D. E. Knuth & O. Patashnik, Concrete Mathematics (1989), Addison-Wesley, Reading, MA. Sections 1.3 & 3.3.

Links

• 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

Crossrefs

Cf. A163782 through A163797 for J_2- through J_17-primes.

Cf. A163799 through A163800 for J_19- through J_20-primes.

Extensions

a(9)-a(11) from Jinyuan Wang, Jul 05 2025