A278334 Numbers k such that (856*10^k - 1) / 9 is prime.

2, 3, 5, 8, 9, 15, 20, 24, 41, 63, 66, 99, 281, 300, 462, 686, 726, 1196, 1574, 2543, 3023, 5322, 12161, 13677, 33797, 137633

Offset: 1

Author

Robert Price, Nov 18 2016

Keywords

• nonn
• more
• hard

Comments

For k >= 0, numbers k such that the digits 95 followed by k occurrences of the digit 1 is prime (see Example section).

a(27) > 2*10^5.

Examples

			3 is in this sequence because (856*10^3 - 1) / 9 = 95111 is prime.
Initial terms and associated primes:
a(1) = 2, 9511;
a(2) = 3, 95111;
a(3) = 5, 9511111;
a(4) = 8, 9511111111;
a(5) = 9, 95111111111; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 951w.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(856*10^# - 1) / 9] &]

PARI

is(n)=ispseudoprime((856*10^n - 1)/9) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(26) from Robert Price, Mar 30 2020