A271882 Numbers k such that (10^k + 101)/3 is prime.

1, 2, 3, 6, 9, 12, 23, 39, 59, 168, 198, 203, 231, 449, 863, 920, 1064, 1484, 1674, 2018, 2943, 3123, 4073, 4122, 8360, 11774, 16031, 26507, 31146, 33170, 44952, 62402, 88020, 89687

Offset: 1

Author

Robert Price, Apr 16 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 67 is prime (see Example section).

a(35) > 2*10^5.

Examples

			3 is in this sequence because (10^3+101)/3 = 367 is prime.
Initial terms and associated primes:
a(1) = 1, 37;
a(2) = 2, 67;
a(3) = 3, 367;
a(4) = 6, 333367;
a(5) = 9, 333333367, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 3w67.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(10^#+101)/3] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime((10^n+101)/3), print1(n, ", "))); \\ Altug Alkan, Apr 16 2016