%I
%S 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 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 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 a(1)=a(2)=1; thereafter a(n) = gpf(a(n1)+a(n2)), where gpf = "greatest prime factor".
%C Rapidly enters a loop with period 3,5,2,7.
%C 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 G. Back and M. Caragiu, <a href="http://www.fq.math.ca/Papers1/484/Back_Caragiu.pdf">The greatest prime factor and recurrent sequences</a>, Fib. Q., 48 (2010), 358362.
%t 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 Cf. A000045, A006530, A020639.
%Y Similar or related sequences: A177904, A177923, A178094, A178095, A178174, A178179, A180101, A180107, A221183.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Dec 16 2010
