A281171 Numbers k such that (5*10^k + 37)/3 is prime.

1, 2, 5, 9, 13, 20, 21, 32, 33, 56, 73, 81, 149, 313, 455, 753, 1013, 1166, 1304, 1679, 15758, 15896, 21801, 41353, 45421, 131090, 151007

Offset: 1

Author

Robert Price, Jan 16 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 79 is prime (see Example section).

a(28) > 2*10^5.

Examples

			2 is in this sequence because (5*10^2 + 37) / 3 = 179 is prime.
Initial terms and associated primes:
a(1) = 1, 29;
a(2) = 2, 179;
a(3) = 5, 166679;
a(4) = 9, 1666666679;
a(5) = 13, 16666666666679; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 16w79.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(5*10^# + 37) / 3] &]

Extensions

a(26)-a(27) from Robert Price, Mar 02 2018