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

1,1

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.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Index entries for primes involving decimal expansion of n

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A228323, A068695.

Sequence in context: A092474 A225851 A107470 * A327122 A071042 A128053

Adjacent sequences: A228322 A228323 A228324 * A228326 A228327 A228328

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 20 2013

Status

approved