

A309321


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


1



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
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OFFSET

1,5


LINKS

Hauke Löffler, Table of n, a(n) for n = 1..1000


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) are 0 primes.
a(6): Between 101 and 131 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


AUTHOR

Hauke Löffler, Jul 23 2019


STATUS

approved



