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 A175723 #36 Jan 05 2025 19:51:39
%S A175723 1,1,2,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,
%T A175723 7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,
%U A175723 5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5,2,7,3,5
%N A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor".
%C A175723 Rapidly enters a loop with period 3,5,2,7.
%C A175723 More generally, if a(1) and a(2) are distinct positive numbers with a(1)+a(2) >= 2, the sequence eventually enters the cycle {7,3,5,2} [Back and Caragiu].
%H A175723 G. Back and M. Caragiu, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/48-4/Back_Caragiu.pdf">The greatest prime factor and recurrent sequences</a>, Fib. Q., 48 (2010), 358-362.
%t A175723 nxt[{a_,b_}]:={b,FactorInteger[a+b][[-1,1]]}; Transpose[NestList[nxt,{1,1},120]][[1]] (* or *) PadRight[{1,1,2},130,{5,2,7,3}] (* _Harvey P. Dale_, Feb 24 2015 *)
%Y A175723 Cf. A000045, A006530, A020639.
%Y A175723 Similar or related sequences: A177904, A177923, A178094, A178095, A178174, A178179, A180101, A180107, A221183.
%K A175723 nonn
%O A175723 1,3
%A A175723 _N. J. A. Sloane_, Dec 16 2010