A163785 a(n) is the n-th J_5-prime (Josephus_5 prime).

3, 15, 17, 45, 73, 83, 165, 177, 181, 229, 377, 383, 787, 2585, 3127, 3635, 4777, 36417, 63337, 166705, 418411

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 5th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_5-prime if this permutation consists of a single cycle of length N.

There are 21 J_5-primes in the interval 2..1000000 only. No formula is known; the J_5-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..21.

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_5-primes are odd.

Crossrefs

Cf. A163782 through A163784 for J_2- through J_4-primes.

Cf. A163786 through A163800 for J_6- through J_20-primes.

Sequence in context: A365371 A080705 A032921 * A080793 A077225 A236526

Adjacent sequences: A163782 A163783 A163784 * A163786 A163787 A163788

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 05 2009

Status

approved