A167023 Fibonacci numbers where both neighbors are semiprimes.

5, 34, 144, 46368

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Oct 27 2009

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A000045, A001358.

Programs

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 *)

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

Formula

A124936 INTERSECT A000045. - R. J. Mathar, Nov 03 2009

Extensions

Edited by R. J. Mathar, Nov 05 2009 and Charles R Greathouse IV, Nov 09 2009