A271505 Numbers k such that (82*10^k + 161)/9 is prime.

1, 2, 4, 5, 7, 8, 14, 17, 22, 49, 130, 136, 142, 170, 196, 220, 967, 1816, 2165, 2542, 2635, 3979, 10319, 11096, 12191, 14381, 14444, 17558, 18230, 42176, 113681

Offset: 1

Author

Robert Price, Apr 08 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 1 followed by the digits 29 is prime (see Example section).

a(32) > 2*10^5.

Examples

			4 is in this sequence because (82*10^4+161)/9 = 91129 is prime.
Initial terms and associated primes:
a(1) = 1, 109;
a(2) = 2, 929;
a(3) = 4, 91129;
a(4) = 5, 911129;
a(5) = 7, 91111129, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 91w29.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(82*10^# + 161)/9] &]

PARI

is(n)=ispseudoprime((82*10^n + 161)/9) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(31) from Robert Price, Oct 31 2019