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 A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor". 18

%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(n-1)+a(n-2)), 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/Papers1/48-4/Back_Caragiu.pdf">The greatest prime factor and recurrent sequences</a>, Fib. Q., 48 (2010), 358-362.

%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

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Last modified October 16 15:27 EDT 2018. Contains 316264 sequences. (Running on oeis4.)