A273728 Numbers k such that (17*10^k + 79)/3 is prime.

1, 2, 3, 5, 7, 12, 37, 45, 55, 139, 205, 264, 445, 975, 1111, 1298, 1340, 1835, 2264, 2317, 2897, 2955, 3001, 4134, 6637, 7063, 20613, 114795, 147890

Offset: 1

Author

Robert Price, May 28 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 93 is prime (see Example section).

a(30) > 3*10^5. - Robert Price, Jul 10 2023

Examples

			3 is in this sequence because (17*10^3+79)/3 = 5693 is prime.
Initial terms and associated primes:
a(1) = 1, 83;
a(2) = 2, 593;
a(3) = 3, 5693;
a(4) = 5, 566693;
a(5) = 7, 56666693, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 56w93.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(17*10^# + 79)/3] &]

PARI

is(n)=ispseudoprime((17*10^n + 79)/3) \\ Charles R Greathouse IV, Jun 08 2016

Extensions

a(28)-a(29) from Robert Price, Apr 15 2019