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%I #35 Jan 21 2023 14:31:08
%S 19,22,31,41,59,107,193,199,227,467
%N Numbers k such that Fibonacci(k) and its reversal are two distinct semiprimes.
%C a(11) > 1000. - _Donovan Johnson_, Jun 06 2009
%C a(11) >= 1801. Inclusion of 1801 depends on the factorization of Fibonacci(1801), a 377-digit composite number. - _Tyler Busby_, Jan 14 2023
%H factordb, <a href="http://factordb.com/index.php?query=I%281801%29">Status of Fibonacci(1801)</a>.
%e F(19) = 4181 = 37 * 113, reverse(F(19)) = 1814 = 2 * 907.
%p with(combinat): with(numtheory): rev:=proc(n) local nn: nn:=convert(n,base,10): add(nn[nops(nn)+1-j]*10^(j-1),j=1..nops(nn)) end: a:=proc(n): if rev(fibonacci(n))<>fibonacci(n) and bigomega(fibonacci(n))=2 and bigomega(rev(fibonacci(n)))=2 then n else fi end: seq(a(n),n=1..200); # _Emeric Deutsch_, Jul 26 2006
%t fspQ[n_]:=Module[{f=Fibonacci[n]},f!=IntegerReverse[f]&&PrimeOmega[f] == PrimeOmega[IntegerReverse[f]]==2]; Select[Range[470],fspQ] (* _Harvey P. Dale_, Jul 24 2016 *)
%o (PARI) is(k) = {(fib=fibonacci(k))!=(fibrev=fromdigits(Vecrev(digits(fib)))) && (bigomega(fib)==2 && bigomega(fibrev)==2)} \\ _Tyler Busby_, Jan 07 2023
%Y F(a(n)) is the intersection of A053409 and A097393
%K nonn,base,more
%O 1,1
%A _Jonathan Vos Post_ and _G. L. Honaker, Jr._, Nov 13 2004
%E More terms from _Emeric Deutsch_, Jul 26 2006
%E a(10) from _Donovan Johnson_, Jun 06 2009
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