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%I #20 Apr 03 2023 10:36:10
%S 4,5,7,11,13,17,47,148091
%N Numbers n for which Lucas(n) and Fibonacci(n) are both prime.
%C The intersection of A001605 and A001606. Fibonacci(148091) and Lucas(148091) are probable primes.
%C Corresponding Fibonacci-Lucas prime twins are listed in A121533. Corresponding Lucas-Fibonacci prime twins are listed in A121534. Fibonacci(148091) and Lucas(148091) are probable Fibonacci-Lucas and Lucas-Fibonacci prime twins. They have 30949 and 30950 digits. - _Alexander Adamchuk_, Aug 05 2006
%C Heuristically, this sequence is finite. It is quite probable, but presently unprovable, that it is now complete. - _David Broadhurst_, Jun 25 2008
%C Western Number Theory problem 007:13 by Gary Walsh asks to prove that a(8) = 148091 is in this sequence. - _Charles R Greathouse IV_, May 21 2014
%H David Broadhurst, <a href="https://t5k.org/curios/page.php?number_id=3994">Prime Curio: 10660...49391 (61899-digits)</a>
%H Gerry Myerson, <a href="http://www.math.colostate.edu/~achter/wntc/problems/problems2007.pdf ">Western Number Theory Problems, 17 & 19 Dec 2007</a>.
%t Select[Range[0, 100], PrimeQ[Fibonacci[#]] && PrimeQ[LucasL[#]] & ] (* _Robert Price_, May 27 2019 *)
%o (PARI) is(n)=isprime(n) && ispseudoprime(fibonacci(n)) && ispseudoprime(fibonacci(n-1)+fibonacci(n+1)) \\ _Charles R Greathouse IV_, May 21 2014
%Y Cf. A001605, A001606, A121533, A121534, A000045, A005478, A000032, A000204, A005479, A080327.
%K hard,nonn,more
%O 1,1
%A _T. D. Noe_, Feb 15 2003
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