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

Author

Henry Bottomley, Jun 19 2000

Keywords

• easy
• nonn

Comments

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

Links

• 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).

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.

Programs

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 *)

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)