A276642 Numbers k such that 3*10^k + 89 is prime.

2, 3, 4, 5, 6, 8, 10, 14, 15, 62, 98, 184, 190, 389, 430, 815, 918, 1124, 1284, 9544, 10068, 16514, 24756, 39880, 86478, 179138

Offset: 1

Author

Robert Price, Mar 23 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 89 is prime (see Example section).

a(27) > 2*10^5.

Examples

			3 is in this sequence because 3*10^3 + 89 = 3089 is prime.
Initial terms and associated primes:
a(1) = 2, 389;
a(2) = 3, 3089;
a(3) = 4, 30089;
a(4) = 5, 300089;
a(5) = 6, 3000089; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 30w89.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[3*10^# + 89] &]

PARI

isok(k) = ispseudoprime(3*10^k + 89); \\ Altug Alkan, Mar 30 2018

Extensions

a(26) from Robert Price, Oct 22 2018