A271821 Numbers k such that (5*10^k - 143)/3 is prime.

3, 4, 5, 6, 10, 23, 30, 33, 64, 189, 207, 213, 463, 547, 1225, 1795, 3726, 3947, 4989, 5226, 9825, 11489, 12666, 14512, 19588, 28795, 29903, 31889, 71357

Offset: 1

Author

Robert Price, Apr 14 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 19 is prime (see Example section).

a(31) > 2*10^5.

Examples

			4 is in this sequence because (5*10^4-143)/3 = 16619 is prime.
Initial terms and associated primes:
a(1) = 3, 1619;
a(2) = 4, 16619;
a(3) = 5, 166619;
a(4) = 6, 1666619;
a(5) = 10, 16666666619, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 16w19.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(5*10^#-143)/3] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime((5*10^n-143)/3), print1(n, ", "))); \\ Altug Alkan, Apr 14 2016