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A163785 a(n) is the n-th J_5-prime (Josephus_5 prime). 2
3, 15, 17, 45, 73, 83, 165, 177, 181, 229, 377, 383, 787, 2585, 3127, 3635, 4777, 36417, 63337, 166705, 418411 (list; graph; refs; listen; history; text; internal format)



Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 5th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_5-prime if this permutation consists of a single cycle of length N.

There are 21 J_5-primes in the interval 2..1000000 only. No formula is known; the J_5-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..21.

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


All J_5-primes are odd.


A163782 through A163784 for J_2- through J_4-primes. A163786 through A163800 for J_6- through J_20-primes.

Sequence in context: A323033 A080705 A032921 * A080793 A077225 A236526

Adjacent sequences:  A163782 A163783 A163784 * A163786 A163787 A163788




Peter R. J. Asveld, Aug 05 2009



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Last modified September 21 20:10 EDT 2021. Contains 347598 sequences. (Running on oeis4.)