A271548 Numbers k such that 4*10^k + 19 is prime.

0, 1, 2, 3, 9, 11, 19, 27, 31, 36, 42, 69, 86, 98, 152, 205, 533, 587, 1302, 1506, 1521, 1573, 1807, 3906, 6461, 9081, 11766, 12595, 15697, 17154, 30507, 36074, 52667, 61367, 122377, 169759

Offset: 1

Author

Robert Price, Apr 09 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 19 is prime (see Example section).

a(37) > 3*10^5.

Examples

			3 is in this sequence because 4*10^3 + 19 = 4019 is prime.
Initial terms and associated primes:
a(1) = 0, 23;
a(2) = 1, 59;
a(3) = 2, 419;
a(4) = 3, 4019;
a(5) = 9, 4000000019, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 40w19.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[4*10^# + 19] &]

PARI

is(n)=ispseudoprime(4*10^n + 19) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(35)-a(36) from Robert Price, Oct 22 2018