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A056531 Sequence remaining after fourth round of Flavius Josephus sieve; remove every fifth term of A056530. 4

%I

%S 1,3,7,13,19,25,27,31,39,43,49,51,61,63,67,73,79,85,87,91,99,103,109,

%T 111,121,123,127,133,139,145,147,151,159,163,169,171,181,183,187,193,

%U 199,205,207,211,219,223,229,231,241,243,247,253,259,265,267,271,279

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

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

%F From _Chai Wah Wu_, Jul 24 2016: (Start)

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

%F 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)

%t 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 *)

%Y 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.

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

%K easy,nonn

%O 1,2

%A _Henry Bottomley_, Jun 19 2000

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)