A163800 a(n) is the n-th J_20-prime (Josephus_20 prime).

2, 5, 30, 54, 81, 109, 149, 186, 513, 1089, 8158, 8533, 17178, 34478, 913274, 976402

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 20th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_20-prime if this permutation consists of a single cycle of length N.

There are 16 J_20-primes in the interval 2..1000000 only. No formula is known; the J_20-primes were 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

2 is a J_20-prime (trivial).

Crossrefs

See A163782 through A163799 for J_2- through J_19-primes.

Sequence in context: A101078 A109739 A261414 * A180826 A367521 A371610

Adjacent sequences: A163797 A163798 A163799 * A163801 A163802 A163803

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 04 2009, Aug 12 2009

Status

approved