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 A307499 #44 May 14 2023 02:33:40 %S A307499 0,1,0,4,4,30,51,230,170,657,216347,3009722,16603784,288244979, %T A307499 4566061654,192922096576,20592039889787,854140717540139, %U A307499 7734073644382760578105 %N A307499 The number of primes between two consecutive prime Lucas numbers, bounds excluded. %H A307499 Kim Walisch, <a href="https://github.com/kimwalisch/primecount">Fast C++ prime counting function implementation (primecount)</a>. %e A307499 a(0): between the first two prime Lucas numbers (2,3) there are 0 primes. %e A307499 a(3): between 11 and 29 there are 4 primes (13, 17, 19, 23). %t A307499 Differences@ PrimePi@ Select[LucasL@ Range[0, 70], PrimeQ] - 1 (* _Giovanni Resta_, Jul 28 2019 *) %o A307499 (SageMath) # uses[A005479] %o A307499 def count_primes_between(a, b): %o A307499 return len(prime_range(a+1, b)) %o A307499 [count_primes_between(A005479[i], A005479[i+1]) for i in range(len(A005479)-1)] %Y A307499 Cf A005479, A134850, A176559. %K A307499 nonn,more %O A307499 1,4 %A A307499 _Hauke Löffler_, Jul 24 2019 %E A307499 a(14)-a(18) from _Giovanni Resta_, Jul 28 2019 %E A307499 a(19) using Kim Walisch's primecount, from _Amiram Eldar_, May 14 2023