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A163786 a(n) is the n-th J_6-prime (Josephus_6 prime). 2
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 (list; graph; refs; listen; history; text; internal format)



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.


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..28.

P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.

Index entries for sequences related to the Josephus Problem


2 is a J_6-prime (trivial).


A163782 through A163785 for J_2- through J_5-primes. 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




Peter R. J. Asveld, Aug 05 2009



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Last modified August 10 08:28 EDT 2020. Contains 336368 sequences. (Running on oeis4.)