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

1,1

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000045, A001358, A006881, A072381.

Column k=2 of A303216.

Sequence in context: A135595 A082483 A075735 * A253910 A144205 A261408

Adjacent sequences: A053406 A053407 A053408 * A053410 A053411 A053412

Keyword

nonn

Author

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

Status

approved