A276470 Numbers k such that (25*10^k + 167) / 3 is prime.

1, 3, 4, 5, 11, 15, 18, 37, 41, 58, 60, 87, 117, 118, 214, 265, 334, 355, 450, 655, 1695, 1734, 2183, 3913, 25313, 32865

Offset: 1

Author

Robert Price, Sep 12 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 89 is prime (see Example section).

a(27) > 2*10^5.

Examples

			3 is in this sequence because (25*10^3 + 167) / 3 = 8389 is prime.
Initial terms and associated primes:
a(1) = 1, 139;
a(2) = 3, 8389
a(3) = 4, 83389;
a(4) = 5, 833389;
a(5) = 11, 833333333389, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 83w89.

Crossrefs

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

Programs

Magma

[n: n in [0..400] |IsPrime((25*10^n + 167) div 3)]; // Vincenzo Librandi, Sep 13 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(25*10^# + 167) / 3] &]

PARI

is(n)=ispseudoprime((25*10^n + 167)/3) \\ Charles R Greathouse IV, Jun 13 2017