A163783 a(n) is the n-th J_3-prime (Josephus_3 prime).

3, 5, 27, 89, 1139, 1219, 1921, 2155, 5775, 9047, 12437, 78785, 105909, 197559, 1062657

Offset: 1

Author

Peter R. J. Asveld, Aug 05 2009

Keywords

• nonn
• more

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 3rd unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_3-prime if this permutation consists of a single cycle of length N.

There are 14 J_3-primes in the interval 2..1000000 only. No formula is known; the J_3-primes have been found by exhaustive search.

a(16) > 3*10^6. - Bert Dobbelaere, Apr 20 2019

Examples

			All J_3-primes are odd.
		

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 the distribution of their prime numbers (2011), TR-CTIT-11-24, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
• P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology.
• P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers Discrete Applied Mathematics 159 (2011) 1915-1932.
• Index entries for sequences related to the Josephus Problem

Crossrefs

A163782 for J_2-primes. A163784 through A163800 for J_4- through J_20-primes.

Extensions

a(15) from Bert Dobbelaere, Apr 20 2019