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

1,5

Links

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

Formula

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

Example

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).

Prog

(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

Crossrefs

Cf. A002385, A037010, A075807, A176559.

Sequence in context: A018816 A040389 A040386 * A104158 A068612 A233820

Adjacent sequences: A309318 A309319 A309320 * A309322 A309323 A309324

Keyword

nonn,base

Author

Hauke Löffler, Jul 23 2019

Status

approved