A291611 Numbers k such that 5*10^k + 81 is prime.

1, 3, 6, 16, 30, 33, 36, 37, 85, 288, 561, 805, 850, 1057, 1192, 1312, 2571, 4579, 5223, 5940, 10191, 18756, 24564, 29595, 43891, 65905, 89118, 97963, 112003, 139945, 174101, 195221

Offset: 1

Author

Robert Price, Aug 27 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 81 is prime (see Example section).

a(33) > 2*10^5.

Examples

			3 is in this sequence because 5*10^3 + 81 = 5081 is prime.
Initial terms and associated primes:
a(1) = 1, 131;
a(2) = 3, 5081;
a(3) = 6, 5000081;
a(4) = 16, 50000000000000081;
a(5) = 30, 5000000000000000000000000000081; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 50w81.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[5*10^# + 81] &]

Extensions

a(29)-a(32) from Robert Price, Mar 04 2019

Terms reordered into ascending order by Robert Price, Apr 03 2022