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A307499
The number of primes between two consecutive prime Lucas numbers, bounds excluded.
1
0, 1, 0, 4, 4, 30, 51, 230, 170, 657, 216347, 3009722, 16603784, 288244979, 4566061654, 192922096576, 20592039889787, 854140717540139, 7734073644382760578105
OFFSET
1,4
EXAMPLE
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).
MATHEMATICA
Differences@ PrimePi@ Select[LucasL@ Range[0, 70], PrimeQ] - 1 (* Giovanni Resta, Jul 28 2019 *)
PROG
(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)]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Hauke Löffler, Jul 24 2019
EXTENSIONS
a(14)-a(18) from Giovanni Resta, Jul 28 2019
a(19) using Kim Walisch's primecount, from Amiram Eldar, May 14 2023
STATUS
approved