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A214320 a(0)=a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-3)), where gpf = "greatest prime factor".

%I A214320 #15 Jul 08 2017 10:52:34
%S A214320 1,1,1,2,3,2,2,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,
%T A214320 5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,
%U A214320 2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3,5,2,5,5,7,3,2,3,3
%N A214320 a(0)=a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-3)), where gpf = "greatest prime factor".
%C A214320 Suggested by A214551 and A177904.
%F A214320 After 7 terms, cycles with period 9.
%p A214320 with(numtheory, divisors); A006530 := proc(n) local i, t1, t2, t3, t4, t5; t1 := divisors(n); t2 := convert(t1, list); t3 := sort(t2); t4 := nops(t3); t5 := 1; for i from 1 to t4 do if isprime(t3[t4+1-i]) then RETURN(t3[t4+1-i]); fi; od; 1; end;
%p A214320 f:=proc(n) option remember; if n <= 2 then 1 else A006530(f(n-1)+f(n-3)); fi; end;
%p A214320 [seq(f(n),n=0..120)];
%t A214320 nxt[{a_,b_,c_}]:={b,c,FactorInteger[c+a][[-1,1]]}; NestList[nxt,{1,1,1},120][[All,1]] (* or *) PadRight[{1,1,1,2,3,2,2},130,{3,2,3,3,5,2,5,5,7}] (* _Harvey P. Dale_, Jul 08 2017 *)
%o A214320 (Haskell)
%o A214320 a214320 n = a214320_list !! n
%o A214320 a214320_list = 1 : 1 : 1 : (map a006530 $
%o A214320    zipWith (+) a214320_list (drop 2 $ a214320_list))
%o A214320 -- _Reinhard Zumkeller_, Jul 24 2012
%Y A214320 Cf. A000930, A006530, A177904, A214320.
%K A214320 nonn
%O A214320 0,4
%A A214320 _N. J. A. Sloane_, Jul 22 2012