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 A144743 #21 Mar 20 2022 04:36:16
%S A144743 3,5,19,341,115939,13441735781,180680260792773944179,
%T A144743 32645356640144805339284259388335434039861,
%U A144743 1065719310162246533488642668727242229836148490441005113524301742665845135502859459
%N A144743 Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=3.
%C A144743 a(0)=3 is the smallest integer generating an increasing sequence of the form a(n)=a(n-1)^2-a(n-1)-1.
%C A144743 Conjecture: A130282 and this sequence are disjoint. If this is true, for n >= 1, a(n+1) is the smallest m such that (m^2-1) / (a(n)^2-1) + 1 is a square. - _Jianing Song_, Mar 19 2022
%F A144743 a(n) = a(n-1)^2-a(n-1)-1, a(0)=3.
%F A144743 a(n) ~ c^(2^n), where c = 2.07259396780115004655284076205241023281287049774423620992171834046728756... . - _Vaclav Kotesovec_, May 06 2015
%t A144743 a = {3}; k = 3; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
%o A144743 (PARI) a(n,s=3)=for(i=1,n,s=s^2-s-1);s \\ _M. F. Hasler_, Oct 06 2014
%Y A144743 Cf. A000058, A082732, A144744, A144745, A144746, A144747, A144748.
%K A144743 nonn
%O A144743 0,1
%A A144743 _Artur Jasinski_, Sep 20 2008
%E A144743 Edited by _M. F. Hasler_, Oct 06 2014