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A056530 Sequence remaining after third round of Flavius Josephus sieve; remove every fourth term of A047241. 7

%I

%S 1,3,7,13,15,19,25,27,31,37,39,43,49,51,55,61,63,67,73,75,79,85,87,91,

%T 97,99,103,109,111,115,121,123,127,133,135,139,145,147,151,157,159,

%U 163,169,171,175,181,183,187,193,195,199,205,207,211,217,219,223,229,231

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

%C Numbers {1, 3, 7} mod 12

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

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

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

%Y 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.

%K easy,nonn

%O 1,2

%A _Henry Bottomley_, Jun 19 2000

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Last modified December 5 22:37 EST 2019. Contains 329782 sequences. (Running on oeis4.)