A282456 Numbers k such that 18*10^k + 1 is prime.

0, 1, 2, 4, 9, 12, 21, 55, 307, 332, 388, 820, 1593, 2432, 2438, 3372, 6270, 7437, 8268, 12135, 16588, 41397, 46126, 47910, 81091

Offset: 1

Author

Robert Price, Feb 15 2017

Keywords

• nonn
• more
• hard

Comments

For k > 0, numbers k such that the digits 18 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(26) > 10^5.

Examples

			2 is in this sequence because 18*10^2 + 1 = 1801 is prime.
Initial terms and associated primes:
a(1) = 0, 19;
a(2) = 1, 181;
a(3) = 2, 1801;
a(4) = 4, 180001;
a(5) = 9, 18000000001; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 180w1.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[18*10^# + 1] &]