A337834 If k is the n-th number ending in 1,3,7, or 9, a(n) is the least prime > k ending in k.

11, 13, 17, 19, 211, 113, 317, 419, 421, 223, 127, 229, 131, 233, 137, 139, 241, 443, 347, 149, 151, 353, 157, 359, 461, 163, 167, 269, 271, 173, 277, 179, 181, 283, 487, 389, 191, 193, 197, 199, 5101, 1103, 5107, 1109, 2111, 2113, 1117, 3119, 3121, 1123, 4127, 1129, 2131, 4133, 2137, 4139, 2141

Offset: 1

Author

Robert Israel, Sep 24 2020

Keywords

• nonn
• base

Comments

a(n) exists by Dirichlet's theorem on primes in arithmetic progressions.

Examples

			For n=3 the third number ending in 1,3,7 or 9 is 7 and the least prime > 7 ending in 7 is a(3)=17.
For n=12 the 12th number ending in 1,3,7 or 9 is 29 and the least prime > 29 ending in 29 is a(12)=229.
		

Links

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

Crossrefs

Cf. A085821, A338715.

Programs

Maple

f:= proc(n) local d, x;
  d:= ilog10(n)+1;
  for x from n + 10^d by 10^d do
    if isprime(x) then return x fi
  od
end proc:
map(f, [seq(seq(10*i+j, j=[1,3,7,9]),i=0..99)];