A048549 -id:A048549 - cp's OEIS frontend

A158191 Attach the smallest prime to the end of the string a(n-1) so a(n) is also prime.

2, 23, 233, 2333, 23333, 2333323, 23333237, 233332373, 23333237353, 2333323735319, 2333323735319149, 2333323735319149571, 23333237353191495713, 23333237353191495713131, 233332373531914957131313

Offset: 1

Sergio Pimentel, Mar 13 2009

a(279) has 1001 digits. - Michael S. Branicky, May 26 2023

			a(6) = 2333323 since a(5) = 23333 (prime) and 233333, 233335, 233337, 2333311, 2333313, 2333317 and 2333319 are all composite.

Michael S. Branicky, Table of n, a(n) for n = 1..278 (terms 1..200 from Harvey P. Dale)

Cf. A048549, A088603, A089703, A065712, A100893.

nxt[n_]:=Module[{k=3},While[CompositeQ[n*10^IntegerLength[k]+k],k = NextPrime[ k]];n*10^IntegerLength[k]+k]; NestList[nxt,2,20] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 13 2019 *)

from itertools import islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p, s = 2, "2"
    while True:
        yield p
        q = 2
        while not isprime(p:=int(s+str(q))):
            q = nextprime(q)
        s += str(q)
print(list(islice(agen(), 15))) # Michael S. Branicky, May 26 2023

More terms from Sean A. Irvine, Nov 29 2009

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).

Original entry on oeis.org

2, 3, 23, 3023, 2393023, 3023172393023, 2393023313023172393023, 3023172393023282393023313023172393023, 239302331302317239302383023172393023282393023313023172393023

Offset: 1

Robert C. Lyons, Jan 30 2023

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

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

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)

cp's OEIS Frontend

A158191 Attach the smallest prime to the end of the string a(n-1) so a(n) is also prime.

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