A163786 a(n) is the n-th J_6-prime (Josephus_6 prime).

2, 13, 17, 18, 34, 49, 93, 97, 106, 225, 401, 745, 2506, 3037, 3370, 4713, 5206, 8585, 13418, 32237, 46321, 75525, 97889, 106193, 238513, 250657, 401902, 490118

Offset

1,1

Comments

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 6th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_6-prime if this permutation consists of a single cycle of length N.

There are 28 J_6-primes in the interval 2..1000000 only. No formula is known; the J_6-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..28.

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_6-prime (trivial).

Crossrefs

Cf. A163782 through A163785 for J_2- through J_5-primes.

Cf. A163787 through A163800 for J_7- through J_20-primes.

Sequence in context: A318911 A065245 A158845 * A153507 A124277 A038889

Adjacent sequences: A163783 A163784 A163785 * A163787 A163788 A163789

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 05 2009

Status

approved