A103544 Least n-digit zeroless prime with nonprime digits.

11, 149, 1181, 11119, 111119, 1111169, 11111119, 111111181, 1111111181, 11111111449, 111111111149, 1111111111441, 11111111111411, 111111111111691, 1111111111111181, 11111111111111119, 111111111111111161

Offset: 2

Author

Ray G. Opao, Mar 22 2005

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 2..999

Programs

Maple

f:= proc(n) local t,x,L,y;
  t:= (10^n-1)/9;
  for x from 0 to 5^n-1 do
    L:= subs({1=3, 2=5, 3=7, 4=8},convert(x,base,5));
    y:= t+add(10^(i-1)*L[i],i=1..nops(L));
    if isprime(y) then return y fi
  od;
  FAIL
end proc:
map(f, [$2..20]); # Robert Israel, Sep 28 2018

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{np = NextPrim[(10^n - 1)/9 - 1]}, While[ Union[ Join[{1, 4, 6, 8, 9}, IntegerDigits[np]]] != {1, 4, 6, 8, 9}, np = NextPrim[np]]; np]; Table[ f[n], {n, 2, 18}] (* Robert G. Wilson v, Mar 23 2005 *)
ndzp[n_]:=Module[{np=NextPrime[FromDigits[PadRight[{},n,1]]]},While[ !SubsetQ[ {1,4,6,8,9},IntegerDigits[ np]],np =NextPrime[np]];np]; Join[{11},Array[ndzp,16,3]] (* Harvey P. Dale, Aug 28 2021 *)

Python

from sympy import isprime
from itertools import product
def a(n):
    for p in product("14689", repeat=n):
        t = int("".join(p))
        if isprime(t): return t
print([a(n) for n in range(2, 22)]) # Michael S. Branicky, Aug 20 2022

Extensions

More terms from Robert G. Wilson v, Mar 23 2005