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 A144838 #28 Jul 13 2025 11:08:40
%S A144838 18,33385282,1384619022984618483717737087933569992335566082
%N A144838 a(n) = Lucas(6^n).
%C A144838 Previous name was: a(n) = round(phi^(6^n)) where phi = 1.6180339887498948482... = (sqrt(5)+1)/2.
%C A144838 General (hyperbolic) trigonometric formula for a(n) = round(phi^((2*k)^n)) = 2*cosh((2*k)^n*arccosh(sqrt(5)/2)) where phi = 1.6180339887498948482... = (sqrt(5)+1)/2. - _Artur Jasinski_, Oct 09 2008
%H A144838 Amiram Eldar, <a href="/A144838/b144838.txt">Table of n, a(n) for n = 1..4</a>
%F A144838 a(n) = G^(6^n) + (1 - G)^(6^n) = G^(6^n) + (-G)^(-6^n) where G is the golden ratio A001622. - _Artur Jasinski_, Oct 05 2008
%F A144838 a(n) = 2*cosh(6^n*arccosh(sqrt(5)/2)). - _Artur Jasinski_, Oct 09 2008
%F A144838 From _Peter Bala_, Nov 28 2022: (Start)
%F A144838 a(n) = Lucas(6^n).
%F A144838 a(n+1) = a(n)^6 - 6*a(n)^4 + 9*a(n)^2 - 2 with a(1) = 18. (End)
%p A144838 a := proc(n) option remember; if n = 1 then 18 else a(n-1)^6 - 6*a(n-1)^4 + 9*a(n-1)^2 - 2 end if; end;
%p A144838 seq(a(n), n = 1..5); # _Peter Bala_, Nov 28 2022
%t A144838 Table[Round[GoldenRatio^(6^n)], {n, 1, 5}]
%t A144838 c = (1 + Sqrt[5])/2; Table[Expand[c^(6^n) + (1 - c)^(6^n)], {n, 1, 5}] (* _Artur Jasinski_, Oct 05 2008 *)
%t A144838 Table[Round[2*Cosh[6^n*ArcCosh[Sqrt[5]/2]]], {n, 1, 4}] (* _Artur Jasinski_, Oct 09 2008 *)
%t A144838 Table[LucasL[6^n], {n, 1, 4}] (* _Amiram Eldar_, Jul 13 2025 *)
%Y A144838 Cf. A001566, A006267, A144836, A144837, A144838, A144839.
%K A144838 nonn
%O A144838 1,1
%A A144838 _Artur Jasinski_, Sep 22 2008
%E A144838 New name from _Peter Bala_, Nov 28 2022