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

1,1

Links

Table of n, a(n) for n=1..9.

Example

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

Prog

(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)

Crossrefs

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

Sequence in context: A092388 A225726 A076530 * A238265 A203015 A260420

Adjacent sequences: A360222 A360223 A360224 * A360226 A360227 A360228

Keyword

nonn,base

Author

Robert C. Lyons, Jan 30 2023

Status

approved