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A167023
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Fibonacci numbers where both neighbors are semiprimes.
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2
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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