A275020 Numbers k such that (5*10^k + 91) / 3 is prime.

1, 2, 3, 10, 19, 35, 43, 80, 107, 143, 199, 218, 255, 304, 353, 560, 904, 996, 1051, 6141, 8075, 9913, 11151, 28469, 75244, 108960, 122592, 178206, 187471, 257431

Offset: 1

Author

Robert Price, Nov 12 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 97 is prime (see Example section).

a(31) > 3*10^5.

Examples

			3 is in this sequence because (5*10^3 + 91) / 3 = 1697 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 197;
a(3) = 3, 1697;
a(4) = 10, 16666666697;
a(5) = 19, 16666666666666666697, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 16w97.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(5*10^# + 91) / 3] &]

PARI

is(n)=ispseudoprime((5*10^n + 91)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(26)-a(29) from Robert Price, Apr 28 2018

a(30) from Robert Price, Oct 25 2023