A272622 Numbers k such that 9*10^k + 19 is prime.

1, 2, 4, 5, 10, 14, 25, 34, 40, 63, 74, 129, 149, 345, 370, 425, 477, 627, 951, 1610, 2564, 2689, 4227, 7300, 7444, 8360, 16541, 21187, 25685, 31803, 89858, 92821

Offset: 1

Author

Robert Price, May 03 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 0 followed by the digits 19 is prime (see Example section).

a(33) > 3*10^5.

Examples

			4 is in this sequence because 9*10^4+19 = 90019 is prime.
Initial terms and associated primes:
a(1) = 1, 109;
a(2) = 2, 919;
a(3) = 4, 90019;
a(4) = 5, 900019;
a(5) = 10, 90000000019, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 90w19.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[9*10^# + 19] &]

PARI

is(n)=ispseudoprime(9*10^n + 19) \\ Charles R Greathouse IV, Jun 13 2017