A309321 The number of primes between two consecutive palindromic primes, bounds excluded.

0, 0, 0, 0, 20, 5, 3, 5, 0, 21, 5, 2, 1, 52, 4, 3, 0, 17, 0, 1104, 21, 7, 73, 9, 105, 35, 8, 54, 51, 11, 34, 43, 78, 8, 52, 29, 19, 10, 80, 50, 22, 33, 78, 53, 9, 994, 11, 17, 26, 7, 20, 49, 75, 12, 109, 100, 27, 16, 12, 16, 32, 48, 28, 69, 32, 42, 6, 56, 48

Offset: 1

Author

Hauke Löffler, Jul 23 2019

Keywords

• nonn
• base

Examples

			a(0): Between the first two palindromic primes (2,3) there are 0 primes.
a(6): Between 101 and 131 there are 5 primes (103, 107, 109, 113, 127).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Hauke Löffler)

Crossrefs

Cf. A002385, A037010, A075807, A176559.

Programs

SageMath

#Palindromic primes
def count_primes_between(a,b):
    return len(prime_range(a+1,b))
[count_primes_between(A002385[i],A002385[i+1]) for i in range (len(A002385)-1)]
# Alternative:
def A309321list(bound):
    L = []; p = 2
    while p < bound:
        p = next_prime(p)
        delta = 0
        while not Word(p.digits()).is_palindrome():
            delta += 1
            p = next_prime(p)
        L.append(delta)
    return L
A309321list(18181) # Peter Luschny, Jul 23 2019

Formula

a(n) = A075807(n+1) - A075807(n) - 1. - Jinyuan Wang, Jul 24 2019