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

Offset

1,1

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.

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..12.

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_16-prime (trivial).

Crossrefs

Cf. A163762 through A163795 for J_2- through J_15-primes.

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

Sequence in context: A330544 A056080 A241232 * A153978 A214908 A143553

Adjacent sequences: A163793 A163794 A163795 * A163797 A163798 A163799

Keyword

nonn,more

Author

Peter R. J. Asveld, Aug 04 2009

Status

approved