A278397 Numbers k such that 10^k - 20001 is prime.

5, 11, 16, 21, 37, 83, 94, 299, 318, 467, 622, 707, 1931, 2175, 2189, 2238, 2526, 5202, 10541, 15822, 17407, 19919, 19998, 25407, 96377, 118009

Offset: 1

Author

Robert Price, Nov 20 2016

Keywords

• nonn
• more
• hard

Comments

For k > 4, numbers k such that k-5 occurrences of the digit 9 followed by the digits 79999 is prime (see Example section).

a(27) > 2*10^5.

Examples

			5 is in this sequence because 10^5 - 20001 = 79999 is prime.
Initial terms and associated primes:
a(1) = 5, 79999;
a(2) = 11, 99999979999;
a(3) = 16, 9999999999979999;
a(4) = 21, 999999999999999979999;
a(5) = 37, 9999999999999999999999999999999979999; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 9w79999.

Crossrefs

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

Programs

Magma

[n: n in [5..400] | IsPrime(10^n - 20001)]; // Vincenzo Librandi, Nov 21 2016

Mathematica

Select[Range[0, 100000], PrimeQ[10^# - 20001] &]

PARI

is(n)=ispseudoprime(10^n-20001) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(26) from Robert Price, Jan 26 2018