A360225 - OEIS

%I #9 Jan 31 2023 08:36:26

%S 2,3,23,3023,2393023,3023172393023,2393023313023172393023,

%T 3023172393023282393023313023172393023,

%U 239302331302317239302383023172393023282393023313023172393023

%N 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 a(4) = 3023 because int(concat('3', '23')) is not prime, and int(concat('3', '0', '23')) is prime.

%o (Python)

%o from sympy import isprime

%o max_n = 10

%o prev_prev = 2

%o prev = 3

%o seq = [prev_prev, prev]

%o for n in range(3, max_n+1):

%o     result = int(str(prev_prev) + str(prev))

%o     if not isprime(result):

%o         middle_length = 1

%o         keep_searching = True

%o         while keep_searching:

%o             for middle in range(0, 10**middle_length):

%o                 result = int(str(prev_prev) + str(middle).zfill(middle_length) + str(prev))

%o                 if isprime(result):

%o                     keep_searching = False

%o                     break

%o             middle_length = middle_length + 1

%o     seq.append(result)

%o     prev_prev = prev

%o     prev = result

%o print(seq)

%Y Cf. A024770, A024785, A048549, A053583, A085823, A211682, A250052,

%K nonn,base

%O 1,1

%A _Robert C. Lyons_, Jan 30 2023