A276845 Numbers k such that (25*10^k - 73) / 3 is prime.

1, 2, 5, 6, 40, 47, 49, 58, 67, 142, 170, 173, 232, 530, 539, 559, 1651, 1858, 2695, 6257, 6714, 8854, 15066, 15091, 16890, 51366, 85249, 135906

Offset: 1

Author

Robert Price, Sep 20 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 09 is prime (see Example section).

a(29) > 2*10^5.

Examples

			2 is in this sequence because (25*10^2 - 73) / 3 = 809 is prime.
Initial terms and associated primes:
a(1) = 1, 59;
a(2) = 2, 809;
a(3) = 5, 833309;
a(4) = 6, 8333309;
a(5) = 40, 83333333333333333333333333333333333333309, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 83w09.

Crossrefs

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

Programs

Magma

[n: n in [0..500] | IsPrime((25*10^n - 73) div 3)]; // Vincenzo Librandi, Sep 22 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(25*10^# - 73) / 3] &]

PARI

is(n) = ispseudoprime((25*10^n - 73) / 3); \\ Altug Alkan, Sep 20 2016

Extensions

a(28) from Robert Price, Sep 22 2019