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%I #15 Mar 21 2016 14:32:00
%S 5,34,144,46368
%N Fibonacci numbers where both neighbors are semiprimes.
%C Next term (if it exists) is larger than 10^10000. I conjecture that this sequence is finite: if neighbors of Fibonacci numbers behave randomly, the expected number of remaining terms is about 0.0103 (or 0.00779 if their behavior mod 6 is taken into account). - _Charles R Greathouse IV_, Nov 09 2009
%F A124936 INTERSECT A000045. - _R. J. Mathar_, Nov 03 2009
%e 5 is in the sequence because 4=2*2 and 6=2*3. 46368 is in the sequence because 46367 = 199 * 233 and 46369 = 89 * 521.
%t u[n_]:=Plus@@Last/@FactorInteger[n]==2; lst={};Do[f=Fibonacci[n];If[u[f-1]&&u[f+1], Print[f];AppendTo[lst,f]],{n,3*5!}];lst
%t Select[Fibonacci[Range[200]],Union[PrimeOmega[#+{1,-1}]]=={2}&] (* _Harvey P. Dale_, Mar 16 2015 *)
%o (PARI) for(n=5,99, f=fibonacci(n); if(bigomega(f-1)==2 && bigomega(f+1)==2, print1(f", "))) \\ _Charles R Greathouse IV_, Mar 21 2016
%Y Cf. A000045, A001358.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009
%E Edited by _R. J. Mathar_, Nov 05 2009 and _Charles R Greathouse IV_, Nov 09 2009
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