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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A127889 A088603 A048549 * A089703 A088094 A112782

Adjacent sequences: A158188 A158189 A158190 * A158192 A158193 A158194

Keyword

nonn,base

Author

Sergio Pimentel, Mar 13 2009

Extensions

More terms from Sean A. Irvine, Nov 29 2009

Status

approved