A307499 The number of primes between two consecutive prime Lucas numbers, bounds excluded.

0, 1, 0, 4, 4, 30, 51, 230, 170, 657, 216347, 3009722, 16603784, 288244979, 4566061654, 192922096576, 20592039889787, 854140717540139, 7734073644382760578105

Offset: 1

Author

Hauke Löffler, Jul 24 2019

Keywords

• nonn
• more

Examples

			a(0): between the first two prime Lucas numbers (2,3) there are 0 primes.
a(3): between 11 and 29 there are 4 primes (13, 17, 19, 23).
		

Links

• Kim Walisch, Fast C++ prime counting function implementation (primecount).

Crossrefs

Cf A005479, A134850, A176559.

Programs

Mathematica

Differences@ PrimePi@ Select[LucasL@ Range[0, 70], PrimeQ] - 1 (* Giovanni Resta, Jul 28 2019 *)

SageMath

# uses[A005479]
def count_primes_between(a, b):
    return len(prime_range(a+1, b))
[count_primes_between(A005479[i], A005479[i+1]) for i in range(len(A005479)-1)]

Extensions

a(14)-a(18) from Giovanni Resta, Jul 28 2019

a(19) using Kim Walisch's primecount, from Amiram Eldar, May 14 2023