A338715 Smallest prime ending with decimal expansion of n, for n relatively prime to 10.

11, 3, 7, 19, 11, 13, 17, 19, 421, 23, 127, 29, 31, 233, 37, 139, 41, 43, 47, 149, 151, 53, 157, 59, 61, 163, 67, 269, 71, 73, 277, 79, 181, 83, 487, 89, 191, 193, 97, 199, 101, 103, 107, 109, 2111, 113, 1117, 3119, 3121, 1123, 127, 1129, 131, 4133, 137, 139, 2141, 2143, 5147, 149, 151, 1153, 157

Offset: 1

Author

N. J. A. Sloane, Nov 11 2020

Keywords

• nonn
• base
• look

Comments

a(n) exists by Dirichlet's theorem.

Links

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

Crossrefs

Cf. A045572, A105888 (base 2 equivalent), A258190.

See A245193, A337834, A338716 for other versions.

Programs

Maple

N:= 100: # for a(1) to a(N)
V:= Vector(N):
count:= 0:
for n from 1 while count < N do
  if igcd(n,10)=1 then
    count:= count+1;
    d:= ilog10(n)+1;
    for x from n by 10^d do
      if isprime(x) then V[count]:= x; break fi
    od
  fi
od:
convert(V,list); # Robert Israel, Nov 11 2020

Python

from sympy import isprime
def a(n):
    ending = 2*n - 1 + (n+1)//4 * 2 # A045572
    i, pow10 = ending, 10**len(str(ending))
    while not isprime(i): i += pow10
    return i
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Nov 03 2021

Extensions

More terms from Robert Israel, Nov 11 2020