

A163784


a(n) is the nth J_4prime (Josephus_4 prime).


2



2, 5, 10, 369, 609, 1841, 2462, 3297, 3837, 14945, 94590, 98121, 965013
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OFFSET

1,1


COMMENTS

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 4th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_4prime if this permutation consists of a single cycle of length N.
There are 13 J_4primes in the interval 2..1000000 only. No formula is known; the J_4primes have been found by exhaustive search.


REFERENCES

P. R. J. Asveld, Permuting Operations on StringsTheir Permutations and Their Primes, Twente University of Technology, 2014; http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.216.1682; http://doc.utwente.nl/67513/1/pospp.pdf.
R. L. Graham, D.E. Knuth & O. Patashnik, Concrete Mathematics (1989), AddisonWesley, Reading, MA. Sections 1.3 & 3.3.


LINKS

Table of n, a(n) for n=1..13.
P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 19151932.


EXAMPLE

2 is a J_4prime (trivial).


CROSSREFS

A163782 through A163783 for J_2 through J_3primes. A163785 through A163800 for J_5 through J_20primes.
Sequence in context: A174475 A133035 A133516 * A215615 A018862 A175310
Adjacent sequences: A163781 A163782 A163783 * A163785 A163786 A163787


KEYWORD

nonn,more


AUTHOR

Peter R. J. Asveld, Aug 05 2009


STATUS

approved



