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 A105285 #14 Sep 05 2019 11:12:51
%S A105285 6,15,18,21,35,39,44,45,54,55,57,78,80,84,90,93,96,117,120,123,132,
%T A105285 133,135,140,147,154,156,162,171,174,195,201,210,213,234,235,240,245,
%U A105285 247,249,252,259,264,273,275,279,286,288,290,291,295,299,312,318,323,327
%N A105285 Indices of Lucas 3-step numbers A001644 which have a nontrivial divisor in common with index.
%C A105285 Extension by _T. D. Noe_. Wanted: closed-form formula for this as exists for Fibonacci and Lucas numbers. See also A105762 (prime Lucas 3-step numbers).
%H A105285 Amiram Eldar, <a href="/A105285/b105285.txt">Table of n, a(n) for n = 1..10000</a>
%F A105285 gcd(a(n), A001644(a(n))) > 1.
%e A105285 gcd(6, A001644(6)) = gcd(6,39) = 3,
%e A105285 gcd(21, A001644(21)) = gcd(21,361109) = 7.
%t A105285 m=300; s = LinearRecurrence[{1, 1, 1}, {3, 1, 3}, m+1]; Select[Range[m], !CoprimeQ[#, s[[#+1]]] &] (* _Amiram Eldar_, Sep 05 2019 *)
%Y A105285 Cf. A001644, A104714, A105762.
%K A105285 easy,nonn
%O A105285 1,1
%A A105285 _Jonathan Vos Post_, Apr 25 2005
%E A105285 More terms from _Amiram Eldar_, Sep 05 2019