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 A349982 #18 Feb 18 2022 23:04:16
%S A349982 1,2,202,301,702,1202,1151,2552,3902,3426,3863,7488,11550,3372,2686,
%T A349982 3228,3156,731,4086,5016,1716,250,1182,915,898,2012,1654,2032,2042,
%U A349982 2236,2338,2486,2611,5296,8106,6900,2700,231,1176,266,302,483,984,688,408,336,230
%N A349982 a(n) = 199 + (a(n-1)+a(n-2))/gcd(a(n-1),a(n-2)), a(0)=1 and a(1)=2.
%C A349982 The sequence repeats periodically with a period of 2920. The first repeating term is a(2785) = 288 = a(5705).
%H A349982 A. Santi on math.stackexchange.com, <a href="https://math.stackexchange.com/questions/4344652/investigating-the-recurrence-relation-x-n1-fracx-nx-n-1x-n-x">Investigating the recurrence relation ...</a>
%e A349982 a(2) = 199+(1+2)/gcd(1,2) = 199+3 = 202,
%e A349982 a(3) = 199+(2+202)/gcd(2,202) = 199+102 = 301.
%t A349982 Nest[Append[#, 199 + Total[#[[-2 ;; -1]]]/(GCD @@ #[[-2 ;; -1]])] &, {1, 2}, 45] (* _Michael De Vlieger_, Jan 08 2022 *)
%K A349982 nonn,easy
%O A349982 0,2
%A A349982 _Augusto Santi_, Jan 08 2022