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A047485 Numbers that are congruent to {0, 3, 5, 7} mod 8.

%I A047485 #26 Sep 08 2022 08:44:57
%S A047485 0,3,5,7,8,11,13,15,16,19,21,23,24,27,29,31,32,35,37,39,40,43,45,47,
%T A047485 48,51,53,55,56,59,61,63,64,67,69,71,72,75,77,79,80,83,85,87,88,91,93,
%U A047485 95,96,99,101,103,104,107,109,111,112,115,117,119,120,123,125
%N A047485 Numbers that are congruent to {0, 3, 5, 7} mod 8.
%H A047485 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047485 From _Colin Barker_, May 14 2012: (Start)
%F A047485 G.f.: x^2*(3+2*x+2*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)).
%F A047485 a(n) = (-5+(-1)^n-i*(-i)^n+i*i^n+8*n)/4 where i=sqrt(-1). (End)
%F A047485 From _Wesley Ivan Hurt_, Jun 04 2016: (Start)
%F A047485 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047485 a(2k) = A004767(k-1) for n>0, a(2k-1) = A047615(k). (End)
%F A047485 E.g.f.: (2 - sin(x) + (4*x - 3)*sinh(x) + (4*x - 2)*cosh(x))/2. - _Ilya Gutkovskiy_, Jun 04 2016
%F A047485 Sum_{n>=2} (-1)^n/a(n) = (8-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - (3-sqrt(2))*Pi/16. - _Amiram Eldar_, Dec 23 2021
%p A047485 A047485:=n->(-5+I^(2*n)-I*(-I)^n+I*I^n+8*n)/4: seq(A047485(n), n=1..100); # _Wesley Ivan Hurt_, Jun 04 2016
%t A047485 Select[Range[0,120], MemberQ[{0,3,5,7}, Mod[#,8]]&] (* _Harvey P. Dale_, May 20 2011 *)
%o A047485 (Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5, 7]]; // _Wesley Ivan Hurt_, Jun 04 2016
%Y A047485 Cf. A004767, A047615.
%K A047485 nonn,easy
%O A047485 1,2
%A A047485 _N. J. A. Sloane_