A289051 Numbers k such that 13*10^k + 1 is prime.

1, 2, 3, 7, 16, 53, 95, 105, 125, 163, 358, 423, 562, 1774, 3459, 13957, 17962, 51179, 65963, 72808

Offset: 1

Author

Robert Price, Jun 22 2017

Keywords

• nonn
• more
• hard

Comments

For k > 0, numbers k such that the digits 13 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(21) > 10^5.

Examples

			2 is in this sequence because 13*10^3 + 1 = 1301 is prime.
Initial terms and associated primes:
a(1) = 1, 131;
a(2) = 2, 1301;
a(3) = 3, 13001;
a(4) = 7, 130000001;
a(5) = 16, 130000000000000001; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 130w1.

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[13*10^# + 1] &]