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 A139563 #13 Jul 01 2022 18:41:44
%S A139563 1,2,3,13,21,34,610,196418,1134903170,20365011074,
%T A139563 15635695580168194910579363790217849593217,
%U A139563 1049252690665646467530632231274619718410203796555123147644873726135009824265250
%N A139563 Fibonacci numbers whose digit sum is a Lucas number.
%C A139563 Depending on whether the Lucas numbers are defined by A000032 or by A000204, one obtains this sequence here or A117766. - _R. J. Mathar_, Nov 03 2008
%C A139563 The next term (a(13)) has 108 digits. - _Harvey P. Dale_, Jul 01 2022
%e A139563 196418 is a Fibonacci number whose digit sum 29 is a Lucas number.
%t A139563 luQ[n_] := n==2 || Block[{i=1}, While[LucasL[i] < n, i++]; LucasL[i] == n]; Select[
%t A139563 Fibonacci[ Range[2, 400]], luQ[ Plus @@ IntegerDigits[#]] &] (* _Giovanni Resta_, Mar 15 2020 *)
%t A139563 Module[{nn=500,ln=LucasL[Range[0,20]]},Select[Fibonacci[Range[nn]],MemberQ[ ln,Total[ IntegerDigits[ #]]]&]]//Union (* _Harvey P. Dale_, Jul 01 2022 *)
%Y A139563 Cf. A000032, A000045, A004090, A117766.
%K A139563 nonn,base,less
%O A139563 1,2
%A A139563 _Parthasarathy Nambi_, Jun 11 2008
%E A139563 1 added in front by _R. J. Mathar_, Nov 03 2008
%E A139563 More terms from _Jinyuan Wang_, Mar 15 2020