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%I #16 Jan 16 2020 17:17:20
%S 1,2,3,5,2,7,9,4,13,17,15,8,23,31,27,29,14,43,57,25,41,33,37,35,18,53,
%T 71,31,51,41,23,16,39,55,47,51,49,25,37,31,17,12,29,41,35,19,27,23,25,
%U 12,37,49,43,23,33,14,47,61,27,22,49,71,30,101,131,58,189,247,109,89
%N a(1)=1, a(2)=2; a(n+2) = (a(n+1) + a(n))/b(n) where b(n) = gcd(a(n+1) + a(n), 4).
%C A Collatz-Fibonacci mixture.
%C Conjecture: sequence diverges to infinity (a(500)=151767071).
%H Ivan Neretin, <a href="/A069227/b069227.txt">Table of n, a(n) for n = 1..10000</a>
%e a(18)=43, a(19)=57, so gcd(a(18) + a(19), 4) = 4 and hence a(20) = 100/4 = 25.
%t Nest[Append[#, #/GCD[#, 4] &[#[[-1]] + #[[-2]]]] &, {1, 2}, 68] (* _Ivan Neretin_, Jun 28 2017 *)
%t nxt[{a_,b_}]:={b,(a+b)/GCD[a+b,4]}; NestList[nxt,{1,2},70][[All,1]] (* _Harvey P. Dale_, Jan 16 2020 *)
%K nonn
%O 1,2
%A _Benoit Cloitre_, Apr 12 2002