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A163792 a(n) is the n-th J_12-prime (Josephus_12 prime). 2
2, 38, 57, 145, 189, 2293, 2898, 6222, 7486, 26793, 45350, 90822, 177773 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Place the numbers 1..N (N>=2) on a circle and cyclicly mark the 12th unmarked number until all N numbers are marked. The order in which the N numbers are marked defines a permutation; N is a J_12-prime if this permutation consists of a single cycle of length N.

There are 13 J_12-primes in the interval 2..1000000 only. No formula is known; the J_12-primes were found by exhaustive search.

REFERENCES

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=10.1.1.216.1682; 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.

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) 1915-1932.

Index entries for sequences related to the Josephus Problem

EXAMPLE

2 is a J_12-prime (trivial).

CROSSREFS

A163782 through A163791 for J_2- through J_11-primes. A163793 through A163800 for J_13- through J_20-primes.

Sequence in context: A284309 A227468 A049487 * A050899 A068401 A173026

Adjacent sequences:  A163789 A163790 A163791 * A163793 A163794 A163795

KEYWORD

nonn,more

AUTHOR

Peter R. J. Asveld, Aug 04 2009

STATUS

approved

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Last modified September 22 15:04 EDT 2021. Contains 347607 sequences. (Running on oeis4.)