A281732 Numbers k such that (8*10^k + 67)/3 is prime.

3, 5, 9, 20, 26, 77, 101, 120, 308, 543, 869, 876, 1193, 1199, 1355, 1923, 3689, 3788, 4182, 6539, 19068, 26922, 38957, 58872, 61230, 72759

Offset: 1

Author

Robert Price, Jan 28 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 6 followed by the digits 89 is prime (see Example section).

a(27) > 2*10^5.

Examples

			5 is in this sequence because (8*10^5 + 67)/3 = 2266689 7751 is prime.
Initial terms and associated primes:
a(1) = 3, 2689;
a(2) = 5, 266689;
a(3) = 9, 2666666689;
a(4) = 20, 266666666666666666689; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 26w89.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(8*10^# + 67)/3] &]