A275236 Numbers k such that (28*10^k - 97)/3 is prime.

1, 5, 8, 20, 27, 56, 74, 81, 107, 217, 294, 326, 525, 645, 667, 764, 863, 1885, 1961, 2913, 3056, 3192, 3327, 5480, 8455, 22797, 50147, 89141, 96265

Offset: 1

Author

Robert Price, Jul 20 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 01 is prime (see Example section).

a(30) > 10^5.

Examples

			5 is in this sequence because (28*10^5-97)/3 = 877 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 5, 933301;
a(3) = 8, 933333301;
a(4) = 20, 933333333333333333301;
a(5) = 27, 9333333333333333333333333301, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 93w01.

Crossrefs

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

Programs

Magma

[n: n in [1..500] | IsPrime((28*10^n-97) div 3)]; // Vincenzo Librandi, Jul 21 2016

Mathematica

Select[Range[0, 100], PrimeQ[(28*10^#-97)/3 && # > 0] &] (* Corrected by Georg Fischer, Jul 22 2019 *)

PARI

is(n)=ispseudoprime((28*10^n-97)/3) \\ Charles R Greathouse IV, Jul 21 2016