A056530 Sequence remaining after third round of Flavius Josephus sieve; remove every fourth term of A047241.

1, 3, 7, 13, 15, 19, 25, 27, 31, 37, 39, 43, 49, 51, 55, 61, 63, 67, 73, 75, 79, 85, 87, 91, 97, 99, 103, 109, 111, 115, 121, 123, 127, 133, 135, 139, 145, 147, 151, 157, 159, 163, 169, 171, 175, 181, 183, 187, 193, 195, 199, 205, 207, 211, 217, 219, 223, 229, 231

Offset

1,2

Comments

Numbers {1, 3, 7} mod 12: A017533, A017557, A017605 interleaved.

Links

Table of n, a(n) for n=1..59.

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

Index entries for sequences related to the Josephus Problem

Formula

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

a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.

G.f.: x*(5*x^3 + 4*x^2 + 2*x + 1)/(x^4 - x^3 - x + 1). (End)

a(n) = 4*n - (13 + 2*A131713(n))/3. - R. J. Mathar, Jun 22 2020

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {1, 3, 7, 13}, 60] (* Harvey P. Dale, Oct 19 2022 *)

Crossrefs

We have A000027 after 0 rounds of sieving, A005408 after 1 round of sieving, 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: A310251 A035496 A310252 * A341447 A310253 A092734

Adjacent sequences: A056527 A056528 A056529 * A056531 A056532 A056533

Keyword

easy,nonn

Author

Henry Bottomley, Jun 19 2000

Status

approved