A305740 a(n) is the smallest k such that 10^m*k + 1 is prime for all m in 1..n.

1, 1, 4, 7, 7, 170716, 170926, 26373004, 247201983, 10562770680, 118345066231, 54717848613610

Offset: 1

Author

Jon E. Schoenfield, Jun 23 2018

Keywords

• nonn
• hard
• more

Comments

a(12) > 3*10^11.

Examples

			10^1*1 + 1 = 11 (prime), so a(1) = 1.
10^2*1 + 1 = 101 (also prime), so a(2) = 1 as well.
10^3*1 + 1 = 1001 = 7*143, so a(3) > 1;
10^1*2 + 1 = 21 = 3*7, so a(3) > 2;
10^2*3 + 1 = 301 = 7*43, so a(3) > 3;
however, for m = 1..3, 10^m*4 + 1 yields 41, 401, and 4001, each of which is prime, so a(3) = 4.
		

Crossrefs

Cf. A000040 (primes), A124417, A124516.

Extensions

a(12) from Giovanni Resta, Jun 25 2018