cp's OEIS Frontend

A360225 a(1) = 2, a(2) = 3, a(n) = the smallest prime whose digits consist of a(n-2), followed by zero or more digits, followed by a(n).

%I A360225 #9 Jan 31 2023 08:36:26
%S A360225 2,3,23,3023,2393023,3023172393023,2393023313023172393023,
%T A360225 3023172393023282393023313023172393023,
%U A360225 239302331302317239302383023172393023282393023313023172393023
%N A360225 a(1) = 2, a(2) = 3, a(n) = the smallest prime whose digits consist of a(n-2), followed by zero or more digits, followed by a(n).
%e A360225 a(4) = 3023 because int(concat('3', '23')) is not prime, and int(concat('3', '0', '23')) is prime.
%o A360225 (Python)
%o A360225 from sympy import isprime
%o A360225 max_n = 10
%o A360225 prev_prev = 2
%o A360225 prev = 3
%o A360225 seq = [prev_prev, prev]
%o A360225 for n in range(3, max_n+1):
%o A360225     result = int(str(prev_prev) + str(prev))
%o A360225     if not isprime(result):
%o A360225         middle_length = 1
%o A360225         keep_searching = True
%o A360225         while keep_searching:
%o A360225             for middle in range(0, 10**middle_length):
%o A360225                 result = int(str(prev_prev) + str(middle).zfill(middle_length) + str(prev))
%o A360225                 if isprime(result):
%o A360225                     keep_searching = False
%o A360225                     break
%o A360225             middle_length = middle_length + 1
%o A360225     seq.append(result)
%o A360225     prev_prev = prev
%o A360225     prev = result
%o A360225 print(seq)
%Y A360225 Cf. A024770, A024785, A048549, A053583, A085823, A211682, A250052,
%K A360225 nonn,base
%O A360225 1,1
%A A360225 _Robert C. Lyons_, Jan 30 2023