%I #14 May 17 2023 09:25:02
%S 1,4,5,9,7,4,11,15,13,7,5,3,2,5,7,3,5,2,7,9,4,13,17,15,8,23,31,27,29,
%T 14,43,57,25,41,33,37,35,18,53,71,31,51,41,23,16,39,55,47,51,49,25,37,
%U 31,17,12,29,41,35,19,27,23,25,12,37,49,43,23,33,14,47,61,27,22,49,71
%N a(1)=1, a(2)=4, 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. Conjecture : sequence diverges to infinity.
%H Robert Israel, <a href="/A069228/b069228.txt">Table of n, a(n) for n = 1..10000</a>
%e a(4)=9 a(5)=7 so gcd(a(4)+a(5),4)=4 and hence a(6)=16/4=4.
%p f:= proc(n) option remember;
%p (procname(n-1)+procname(n-2))/igcd(procname(n-1)+procname(n-2),4)
%p end proc:
%p f(1):= 1: f(2):= 4:
%p map(f, [$1..100]); # _Robert Israel_, Jan 05 2018
%t a[n_] := a[n] = Switch[n, 1, 1, 2, 4, _, (a[n-1] + a[n-2])/GCD[a[n-1] + a[n-2], 4]];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, May 17 2023 *)
%K nonn
%O 1,2
%A _Benoit Cloitre_, Apr 12 2002