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

1,1

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

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

Prog

(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

Crossrefs

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

See A245193, A337834, A338716 for other versions.

Sequence in context: A344542 A334132 A245193 * A258190 A244471 A083968

Adjacent sequences: A338712 A338713 A338714 * A338716 A338717 A338718

Keyword

nonn,base,look

Author

N. J. A. Sloane, Nov 11 2020.

Extensions

More terms from Robert Israel, Nov 11 2020

Status

approved