A293531 Numbers k such that (268*10^k - 1)/3 is prime.

0, 2, 6, 7, 12, 13, 17, 18, 26, 77, 151, 222, 403, 567, 1107, 7221, 7722, 8475, 9729, 17904, 21404, 30170, 62523

Offset: 1

Author

Robert Price, Oct 11 2017

Keywords

• nonn
• more
• hard

Comments

Numbers k such that the digits 89 followed by k occurrences of the digit 3 is prime (see Example section).

a(24) > 10^5.

Examples

			2 is in this sequence because (268*10^2 - 1)/3 = 8933 is prime.
Initial terms and associated primes:
a(1) = 0, 89;
a(2) = 2, 8933;
a(3) = 6, 89333333;
a(4) = 7, 893333333;
a(5) = 12, 89333333333333; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 893w.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(268*10^# - 1)/3] &]

PARI

isok(k) = isprime((268*10^k - 1)/3); \\ Altug Alkan, Oct 11 2017