A053409 - OEIS

%I #32 Jun 26 2020 19:01:45

%S 21,34,55,377,4181,17711,121393,1346269,5702887,165580141,53316291173,

%T 956722026041,2504730781961,308061521170129,806515533049393,

%U 14472334024676221,1779979416004714189,19740274219868223167,573147844013817084101,10284720757613717413913

%N Fibonacci numbers which are semiprimes.

%C Subsequence of A006881, since the only square Fibonacci numbers are 1 and 144. - _Charles R Greathouse IV_, Sep 24 2012

%C 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

%H Vincenzo Librandi, <a href="/A053409/b053409.txt">Table of n, a(n) for n = 1..48</a>

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

%t Select[Fibonacci@Range[120],Last/@FactorInteger[#]=={1,1}&] (* _Vladimir Joseph Stephan Orlovsky_, Jan 29 2012 *)

%t Select[Fibonacci[Range[150]],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Jun 26 2020 *)

%o (PARI) issemi(n)=bigomega(n)==2

%o 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

%Y Cf. A000045, A001358, A006881, A072381.

%Y Column k=2 of A303216.

%K nonn

%O 1,1

%A _G. L. Honaker, Jr._, Jan 09 2000