A163785 -id:A163785 - cp's OEIS frontend

A163784 a(n) is the n-th J_4-prime (Josephus_4 prime).

2, 5, 10, 369, 609, 1841, 2462, 3297, 3837, 14945, 94590, 98121, 965013, 1634157

Offset: 1

Peter R. J. Asveld, Aug 05 2009

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.
a(15) > 3*10^6. - Bert Dobbelaere, Apr 20 2019

			2 is a J_4-prime (trivial).

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

P. R. J. Asveld, Permuting operations on strings and the distribution of their prime numbers (2011), TR-CTIT-11-24, Dept. of CS, Twente University of Technology, Enschede, The Netherlands.
P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology.
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

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

a(14) from Bert Dobbelaere, Apr 20 2019

A163786 a(n) is the n-th J_6-prime (Josephus_6 prime).

Original entry on oeis.org

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

Offset: 1

Peter R. J. Asveld, Aug 05 2009

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.

			2 is a J_6-prime (trivial).

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

P. R. J. Asveld, Permuting Operations on Strings and Their Relation to Prime Numbers, Discrete Applied Mathematics 159 (2011) 1915-1932.
P. R. J. Asveld, Permuting Operations on Strings-Their Permutations and Their Primes, Twente University of Technology, 2014. University link.
Index entries for sequences related to the Josephus Problem

Cf. A163782 through A163785 for J_2- through J_5-primes.

Cf. A163787 through A163800 for J_7- through J_20-primes.

cp's OEIS Frontend

A163784 a(n) is the n-th J_4-prime (Josephus_4 prime).

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