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%I #17 Sep 08 2022 08:44:57
%S 2,3,4,5,7,10,11,12,13,15,18,19,20,21,23,26,27,28,29,31,34,35,36,37,
%T 39,42,43,44,45,47,50,51,52,53,55,58,59,60,61,63,66,67,68,69,71,74,75,
%U 76,77,79,82,83,84,85,87,90,91,92,93,95,98,99,100,101,103
%N Numbers that are congruent to {2, 3, 4, 5, 7} mod 8.
%H Vincenzo Librandi, <a href="/A047502/b047502.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+x+x^2+x^3+2*x^4+x^5) ) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Nov 06 2015
%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 - 15 - 2*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) - 7*((n+4) mod 5))/25.
%F a(5k) = 8k-1, a(5k-1) = 8k-3, a(5k-2) = 8k-4, a(5k-3) = 8k-5, a(5k-4) = 8k-6. (End)
%p A047502:=n->8*floor(n/5)+[(2, 3, 4, 5, 7)][(n mod 5)+1]: seq(A047502(n), n=0..100); # _Wesley Ivan Hurt_, Jul 31 2016
%t Select[Range[0, 100], MemberQ[{2, 3, 4, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jul 31 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [2, 3, 4, 5, 7]]; // _Wesley Ivan Hurt_, Jul 31 2016
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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