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A214094 a(0)=0, a(1)=1; a(n)=a(n-1)+a(n-2) if a(n-1)+a(n-2) is not semiprime; otherwise a(n) is the largest prime divisor of a(n-1)+a(n-2).

%I A214094 #19 Nov 13 2017 10:13:58
%S A214094 0,1,1,2,3,5,8,13,7,20,27,47,37,84,11,19,30,7,37,44,81,125,103,228,
%T A214094 331,43,374,139,513,652,233,885,1118,2003,3121,5124,8245,461,8706,103,
%U A214094 383,486,79,113,192,61,23,84,107,191,149,340,163,503,666,167,833,1000,1833,2833,2333,5166,7499
%N A214094 a(0)=0, a(1)=1; a(n)=a(n-1)+a(n-2) if a(n-1)+a(n-2) is not semiprime; otherwise a(n) is the largest prime divisor of a(n-1)+a(n-2).
%C A214094 An analog of the Fibonacci numbers A000045 without semiprimes.
%C A214094 Is the sequence unbounded? (Cf. a dual sequence A214156 which is bounded.)
%H A214094 Peter J. C. Moses, <a href="/A214094/b214094.txt">Table of n, a(n) for n = 0..499</a>
%p A214094 A214094 := proc(n)
%p A214094     option remember ;
%p A214094     if n <=1 then
%p A214094         n;
%p A214094     else
%p A214094         a := procname(n-1)+procname(n-2) ;
%p A214094         if numtheory[bigomega](a) =2 then
%p A214094             max(op(numtheory[factorset](a)));
%p A214094         else
%p A214094             return a;
%p A214094         end if;
%p A214094     end if;
%p A214094 end proc: # _R. J. Mathar_, Feb 18 2013
%t A214094 A214094[0]:=0;
%t A214094 A214094[1]:=1;
%t A214094 A214094[n_]:=A214094[n]=If[PrimeOmega[#]==2,Last[Most[Divisors[#]]],#]&[A214094[n-1]+A214094[n-2]];
%t A214094 Table[A214094[n],{n,0,99}] (* _Peter J. C. Moses_, Feb 18 2013 *)
%t A214094 nxt[{a_,b_}]:={b,If[PrimeOmega[a+b]==2,FactorInteger[a+b][[-1,1]],a+b]}; NestList[nxt,{0,1},70][[All,1]] (* _Harvey P. Dale_, Nov 13 2017 *)
%Y A214094 Cf. A001358, A214156.
%K A214094 nonn
%O A214094 0,4
%A A214094 _Vladimir Shevelev_, Feb 16 2013