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 A167023 Fibonacci numbers where both neighbors are semiprimes. 2
 5, 34, 144, 46368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Table of n, a(n) for n=1..4. FORMULA A124936 INTERSECT A000045. - R. J. Mathar, Nov 03 2009 EXAMPLE 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. MATHEMATICA 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 Select[Fibonacci[Range[200]], Union[PrimeOmega[#+{1, -1}]]=={2}&] (* Harvey P. Dale, Mar 16 2015 *) PROG (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 CROSSREFS Cf. A000045, A001358. Sequence in context: A135973 A186636 A034224 * A316559 A284850 A248373 Adjacent sequences: A167020 A167021 A167022 * A167024 A167025 A167026 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Oct 27 2009 EXTENSIONS Edited by R. J. Mathar, Nov 05 2009 and Charles R Greathouse IV, Nov 09 2009 STATUS approved

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