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).
2, 3, 23, 3023, 2393023, 3023172393023, 2393023313023172393023, 3023172393023282393023313023172393023, 239302331302317239302383023172393023282393023313023172393023
Offset: 1
Examples
a(4) = 3023 because int(concat('3', '23')) is not prime, and int(concat('3', '0', '23')) is prime.
Programs
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Python
from sympy import isprime max_n = 10 prev_prev = 2 prev = 3 seq = [prev_prev, prev] for n in range(3, max_n+1): result = int(str(prev_prev) + str(prev)) if not isprime(result): middle_length = 1 keep_searching = True while keep_searching: for middle in range(0, 10**middle_length): result = int(str(prev_prev) + str(middle).zfill(middle_length) + str(prev)) if isprime(result): keep_searching = False break middle_length = middle_length + 1 seq.append(result) prev_prev = prev prev = result print(seq)