%N Fibonacci primes or semiprimes F(k) such that F(k+1) is again prime or semiprime.
%C By definition, the smaller number in a pair of two consecutive Fibonacci numbers in A061305. a(9), if it exists, is >= A000045(230), so it has at least 48 digits. [From _R. J. Mathar_, Feb 06 2010]
%C A search for consecutive numbers in the union of A072381 and A001605 shows that a(9) must be larger than A000045(990), a number with 207 digits, if it exists. [From _R. J. Mathar_, Jun 02 2010]
%F Let F(n) = n-th Fibonacci number and define a 2-almost prime number to be a number with only 2 prime divisors with multiplicity.
%e (55,89) is an almost twin Fibonacci prime pair because 55=5*11 is a 2-almost prime and 89 is prime.
%o (PARI) ATfib(n) = for(x=3,n,f1=fibonacci(x);f2=fibonacci(x+1);if(bigomega (f1)<=2&&bigomega(f2)<=2, print1(f1",")))
%o (PARI) for( k=3,10^5, bigomega( fibonacci( k++ ))>2 & next; bigomega( fibonacci( k-1 ))>2 & next; print1(fibonacci(k--)",")) \\ - M. F. Hasler, May 01 2008
%Y Cf. A001358.
%Y Cf. A053409, A005478. [From _R. J. Mathar_, Jun 02 2010]
%Y Cf. A001605, A072381, A278637.
%A _Cino Hilliard_, Mar 28 2008
%E Edited by _M. F. Hasler_, May 01 2008