A281734 Numbers k such that (2*10^k + 529)/9 is prime.

0, 1, 3, 4, 7, 9, 16, 18, 21, 33, 34, 45, 49, 57, 567, 595, 685, 867, 1867, 4204, 5311, 11493, 13923, 19116, 30471, 32038, 34551, 99408, 113631, 134364, 195399

Offset: 1

Author

Robert Price, Jan 28 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that k-2 occurrences of the digit 2 followed by the digits 81 is prime (see Example section).

a(32) > 2*10^5.

Examples

			3 is in this sequence because (2*10^3 + 529)/9 = 281 is prime.
Initial terms and associated primes:
a(1) = 0, 59;
a(2) = 1, 61;
a(3) = 3, 281;
a(4) = 4, 2281;
a(5) = 7, 2222281; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 2w81.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(2*10^# + 529)/9] &]

Extensions

a(29)-a(31) from Robert Price, Jan 02 2018