cp's OEIS Frontend

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

%I A309321 #39 May 14 2023 04:14:09
%S A309321 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,
%T A309321 51,11,34,43,78,8,52,29,19,10,80,50,22,33,78,53,9,994,11,17,26,7,20,
%U A309321 49,75,12,109,100,27,16,12,16,32,48,28,69,32,42,6,56,48
%N A309321 The number of primes between two consecutive palindromic primes, bounds excluded.
%H A309321 Amiram Eldar, <a href="/A309321/b309321.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Hauke Löffler)
%F A309321 a(n) = A075807(n+1) - A075807(n) - 1. - _Jinyuan Wang_, Jul 24 2019
%e A309321 a(0): Between the first two palindromic primes (2,3) there are 0 primes.
%e A309321 a(6): Between 101 and 131 there are 5 primes (103, 107, 109, 113, 127).
%o A309321 (SageMath)
%o A309321 #Palindromic primes
%o A309321 def count_primes_between(a,b):
%o A309321     return len(prime_range(a+1,b))
%o A309321 [count_primes_between(A002385[i],A002385[i+1]) for i in range (len(A002385)-1)]
%o A309321 # Alternative:
%o A309321 def A309321list(bound):
%o A309321     L = []; p = 2
%o A309321     while p < bound:
%o A309321         p = next_prime(p)
%o A309321         delta = 0
%o A309321         while not Word(p.digits()).is_palindrome():
%o A309321             delta += 1
%o A309321             p = next_prime(p)
%o A309321         L.append(delta)
%o A309321     return L
%o A309321 A309321list(18181) # _Peter Luschny_, Jul 23 2019
%Y A309321 Cf. A002385, A037010, A075807, A176559.
%K A309321 nonn,base
%O A309321 1,5
%A A309321 _Hauke Löffler_, Jul 23 2019