A163796 a(n) is the n-th J_16-prime (Josephus_16 prime).

2, 14, 49, 333, 534, 550, 2390, 3682, 146794, 275530, 687245, 855382, 2827062, 3062118, 3805189

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 16th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_16-prime if this permutation consists of a single cycle of length N.

There are 12 J_16-primes in the interval 2..1000000 only. No formula is known; the J_16-primes were found by exhaustive search.

Examples

			2 is a J_16-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 A163795 for J_2- through J_15-primes.

Cf. A163797 through A163800 for J_17- through J_20-primes.

Extensions

a(13)-a(15) from Jinyuan Wang, Jul 03 2025