This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080327 #27 Apr 25 2025 10:29:03 %S A080327 4,5,7,11,13,17,47,148091 %N A080327 Numbers k for which Lucas(k) and Fibonacci(k) are both prime. %C A080327 The intersection of A001605 and A001606. Fibonacci(148091) and Lucas(148091) are probable primes. %C A080327 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 A080327 Heuristically, this sequence is finite. It is quite probable, but presently unprovable, that it is now complete. - _David Broadhurst_, Jun 25 2008 %C A080327 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 %D A080327 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 246. %H A080327 David Broadhurst, <a href="https://t5k.org/curios/page.php?number_id=3994">Prime Curio: 10660...49391 (61899-digits)</a> %H A080327 Gerry Myerson, <a href="http://www.math.colostate.edu/~achter/wntc/problems/problems2007.pdf ">Western Number Theory Problems, 17 & 19 Dec 2007</a>. %t A080327 Select[Range[0, 100], PrimeQ[Fibonacci[#]] && PrimeQ[LucasL[#]] & ] (* _Robert Price_, May 27 2019 *) %o A080327 (PARI) is(n)=isprime(n) && ispseudoprime(fibonacci(n)) && ispseudoprime(fibonacci(n-1)+fibonacci(n+1)) \\ _Charles R Greathouse IV_, May 21 2014 %Y A080327 Cf. A001605, A001606, A121533, A121534, A000045, A005478, A000032, A000204, A005479, A080327. %K A080327 hard,nonn,more %O A080327 1,1 %A A080327 _T. D. Noe_, Feb 15 2003