A056531 Sequence remaining after a fourth round of Flavius Josephus sieve; remove every fifth term of A056530.

1, 3, 7, 13, 19, 25, 27, 31, 39, 43, 49, 51, 61, 63, 67, 73, 79, 85, 87, 91, 99, 103, 109, 111, 121, 123, 127, 133, 139, 145, 147, 151, 159, 163, 169, 171, 181, 183, 187, 193, 199, 205, 207, 211, 219, 223, 229, 231, 241, 243, 247, 253, 259, 265, 267, 271, 279

Offset

1,2

Comments

Numbers {1, 3, 7, 13, 19, 25, 27, 31, 39, 43, 49, 51} mod 60.

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to the Josephus Problem

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Formula

From Chai Wah Wu, Jul 24 2016: (Start)

a(n) = a(n-1) + a(n-12) - a(n-13) for n > 13.

G.f.: x*(9*x^12 + 2*x^11 + 6*x^10 + 4*x^9 + 8*x^8 + 4*x^7 + 2*x^6 + 6*x^5 + 6*x^4 + 6*x^3 + 4*x^2 + 2*x + 1)/(x^13 - x^12 - x + 1). (End)

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 3, 7, 13, 19, 25, 27, 31, 39, 43, 49, 51, 61}, 60] (* Harvey P. Dale, Mar 11 2019 *)

Crossrefs

Compare A000027 for 0 rounds of sieve, A005408 after 1 round of sieve, A047241 after 2 rounds, A056530 after 3 rounds, A056531 after 4 rounds, A000960 after all rounds.

After n rounds the remaining sequence comprises A002944(n) numbers mod A003418(n+1), i.e. 1/(n+1) of them.

Sequence in context: A216098 A310262 A310263 * A310264 A144917 A102828

Adjacent sequences: A056528 A056529 A056530 * A056532 A056533 A056534

Keyword

easy,nonn

Author

Henry Bottomley, Jun 19 2000

Status

approved