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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
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
Sequence in context: A135973 A186636 A034224 * A316559 A284850 A248373
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Nov 05 2009 and Charles R Greathouse IV, Nov 09 2009
STATUS
approved

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Last modified June 12 11:18 EDT 2024. Contains 373331 sequences. (Running on oeis4.)