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A163784 a(n) is the n-th J_4-prime (Josephus_4 prime). 2
2, 5, 10, 369, 609, 1841, 2462, 3297, 3837, 14945, 94590, 98121, 965013 (list; graph; refs; listen; history; text; internal format)



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_4-prime if this permutation consists of a single cycle of length N.

There are 13 J_4-primes in the interval 2..1000000 only. No formula is known; the J_4-primes have been found by exhaustive search.


P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology, 2014; http://citeseerx.ist.psu.edu/viewdoc/summary?doi=; http://doc.utwente.nl/67513/1/pospp.pdf.

R. L. Graham, D.E. Knuth & O. Patashnik, Concrete Mathematics (1989), Addison-Wesley, Reading, MA. Sections 1.3 & 3.3.


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) 1915-1932.


2 is a J_4-prime (trivial).


A163782 through A163783 for J_2- through J_3-primes. A163785 through A163800 for J_5- through J_20-primes.

Sequence in context: A174475 A133035 A133516 * A215615 A018862 A175310

Adjacent sequences:  A163781 A163782 A163783 * A163785 A163786 A163787




Peter R. J. Asveld, Aug 05 2009



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Last modified February 7 22:38 EST 2016. Contains 268087 sequences.