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%I #23 Sep 08 2022 08:44:57
%S 0,2,3,5,7,8,10,11,13,15,16,18,19,21,23,24,26,27,29,31,32,34,35,37,39,
%T 40,42,43,45,47,48,50,51,53,55,56,58,59,61,63,64,66,67,69,71,72,74,75,
%U 77,79,80,82,83,85,87,88,90,91,93,95,96,98,99,101,103
%N Numbers that are congruent to {0, 2, 3, 5, 7} mod 8.
%H Vincenzo Librandi, <a href="/A047488/b047488.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F G.f.: x^2*(2+x+2*x^2+2*x^3+x^4)/((1-x)^2*(1+x+x^2+x^3+x^4)). [_Colin Barker_, May 14 2012]
%F From _Wesley Ivan Hurt_, Jul 31 2016: (Start)
%F a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.
%F a(n) = (40*n - 35 - 2*(n mod 5) - 2*((n+1) mod 5) + 3*((n+2) mod 5) - 2*((n+3) mod 5) + 3*((n+4) mod 5))/25.
%F a(5k) = 8k-1, a(5k-1) = 8k-3, a(5k-2) = 8k-5, a(5k-3) = 8k-6, a(5k-4) = 8k-8. (End)
%p A047488:=n->8*floor(n/5)+[(0, 2, 3, 5, 7)][(n mod 5)+1]: seq(A047488(n), n=0..100); # _Wesley Ivan Hurt_, Jul 31 2016
%t Select[Range[0,150], MemberQ[{0, 2, 3, 5, 7}, Mod[#,8]]&] (* _Harvey P. Dale_, Mar 20 2011 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3, 5, 7]]; // _Wesley Ivan Hurt_, Jul 31 2016
%Y Different from A022342.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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