A275096 Numbers k such that 2*10^k + 89 is prime.

1, 3, 4, 8, 9, 10, 13, 20, 27, 74, 89, 93, 137, 139, 296, 310, 662, 749, 1249, 2540, 2848, 3309, 8677, 11573, 15286, 17125, 39526, 42187, 44476, 47823, 92897

Offset: 1

Author

Robert Price, Jul 16 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 0 followed by the digits 89 is prime (see Example section).

a(32) > 10^5.

Examples

			3 is in this sequence because 2*10^3 + 89 = 2089 is prime.
Initial terms and associated primes:
a(1) = 1, 109;
a(2) = 3, 2089;
a(3) = 4, 20089;
a(4) = 8, 200000089;
a(5) = 9, 2000000089, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 20w89.

Crossrefs

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

Programs

Magma

[n: n in [1..500] | IsPrime(2*10^n+89)]; // Vincenzo Librandi, Jul 17 2016

Mathematica

Select[Range[0, 100000], PrimeQ[2*10^# + 89] &]

PARI

is(n)=ispseudoprime(2*10^n+89) \\ Charles R Greathouse IV, Jun 13 2017