A053409 Fibonacci numbers which are semiprimes.

21, 34, 55, 377, 4181, 17711, 121393, 1346269, 5702887, 165580141, 53316291173, 956722026041, 2504730781961, 308061521170129, 806515533049393, 14472334024676221, 1779979416004714189, 19740274219868223167, 573147844013817084101, 10284720757613717413913

Offset: 1

Author

G. L. Honaker, Jr., Jan 09 2000

Keywords

• nonn

Comments

Subsequence of A006881, since the only square Fibonacci numbers are 1 and 144. - Charles R Greathouse IV, Sep 24 2012

Apart from a(1) = 21, all terms are of the form F(p), F(2p), or F(p^2) where F(n) is the n-th Fibonacci number. - Charles R Greathouse IV, Oct 06 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A000045, A001358, A006881, A072381.

Column k=2 of A303216.

Programs

Mathematica

Select[Fibonacci@Range[120],Last/@FactorInteger[#]=={1,1}&] (* Vladimir Joseph Stephan Orlovsky, Jan 29 2012 *)
Select[Fibonacci[Range[150]],PrimeOmega[#]==2&] (* Harvey P. Dale, Jun 26 2020 *)

PARI

issemi(n)=bigomega(n)==2
list(lim)=my(v=List([21]),F,t); forprime(p=2,, F=fibonacci(p); if(F>lim, break); if(issemi(F), listput(v,F))); forprime(p=2,, F=fibonacci(p^2); if(F>lim, break); if(isprime(t=fibonacci(p)) && isprime(F/t), listput(v,F))); forprime(p=2,, F=fibonacci(2*p); if(F>lim, break); if(isprime(t=fibonacci(p)) && isprime(F/t), listput(v,F))); Set(v) \\ Charles R Greathouse IV, Oct 06 2016

Formula

a(n) = A000045(A072381(n)).