A228325 a(n) is the smallest number m>n such that the concatenation nm is prime.

3, 3, 7, 7, 9, 7, 9, 9, 11, 13, 17, 13, 19, 23, 23, 19, 21, 23, 31, 27, 29, 37, 33, 37, 31, 33, 29, 33, 39, 37, 37, 51, 43, 49, 39, 37, 39, 47, 43, 49, 53, 43, 49, 47, 47, 49, 51, 61, 51, 51, 53, 61, 81, 71, 57, 57, 79, 61, 81, 67, 63, 63, 67, 69, 69, 73, 79

Offset: 1

Author

N. J. A. Sloane, Aug 20 2013

Keywords

• nonn
• base

Comments

Max Alekseyev (see link in A068695) shows that a(n) always exists. - N. J. A. Sloane, Nov 13 2020

Suggested by the existence question in A228323.

Examples

			12 is not prime but 13 is, so a(1)=3.
23 is prime so a(2)=3.
34, 35, 36 are not prime but 37 is, so a(3)=7.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Index entries for primes involving decimal expansion of n

Crossrefs

Cf. A228323, A068695.

Programs

Mathematica

smc[n_]:=Module[{m=n+1},If[OddQ[n],m++];While[!PrimeQ[n*10^IntegerLength[ m]+ m],m=m+2];m]; Array[smc,70] (* Harvey P. Dale, Apr 30 2016 *)

Python

from sympy import isprime
from itertools import count
def a(n): return next(k for k in count(n+1) if isprime(int(str(n)+str(k))))
print([a(n) for n in range(1, 68)]) # Michael S. Branicky, Oct 18 2022