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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).
0
2, 3, 23, 3023, 2393023, 3023172393023, 2393023313023172393023, 3023172393023282393023313023172393023, 239302331302317239302383023172393023282393023313023172393023
OFFSET
1,1
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)
KEYWORD
nonn,base
AUTHOR
Robert C. Lyons, Jan 30 2023
STATUS
approved