This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047365 #19 Apr 25 2024 09:21:49
%S A047365 0,3,4,5,7,10,11,12,14,17,18,19,21,24,25,26,28,31,32,33,35,38,39,40,
%T A047365 42,45,46,47,49,52,53,54,56,59,60,61,63,66,67,68,70,73,74,75,77,80,81,
%U A047365 82,84,87,88,89,91,94,95,96,98,101,102,103,105,108,109,110
%N A047365 Numbers that are congruent to {0, 3, 4, 5} mod 7.
%H A047365 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047365 G.f.: x^2*(3+x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F A047365 a(1)=0, a(2)=3, a(3)=4, a(4)=5, a(5)=7, a(n)=a(n-1)+a(n-4)-a(n-5) for n>5. - _Harvey P. Dale_, May 26 2012
%F A047365 From _Wesley Ivan Hurt_, Jun 04 2016: (Start)
%F A047365 a(n) = (14*n-11+i^(2*n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).
%F A047365 a(2k) = A047389(k), a(2k-1) = A047345(k). (End)
%p A047365 A047365:=n->(14*n-11+I^(2*n)-(3+I)*I^(-n)-(3-I)*I^n)/8: seq(A047365(n), n=1..100); # _Wesley Ivan Hurt_, Jun 04 2016
%t A047365 Select[Range[0,100], MemberQ[{0,3,4,5}, Mod[#,7]]&] (* or *) LinearRecurrence[{1,0,0,1,-1}, {0,3,4,5,7}, 60] (* _Harvey P. Dale_, May 26 2012 *)
%o A047365 (Magma) [n : n in [0..150] | n mod 7 in [0, 3, 4, 5]]; // _Wesley Ivan Hurt_, Jun 04 2016
%Y A047365 Cf. A047345, A047389.
%K A047365 nonn,easy
%O A047365 1,2
%A A047365 _N. J. A. Sloane_