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

Author

Sergio Pimentel, Mar 13 2009

Keywords

• nonn
• base

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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 *)

Python

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

Extensions

More terms from Sean A. Irvine, Nov 29 2009