

A167023


Fibonacci numbers where both neighbors are semiprimes.


2




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[f1]&&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(f1)==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



