A290964 Numbers k such that (35*10^k - 593)/9 is prime.

3, 5, 6, 14, 24, 84, 87, 207, 734, 797, 1743, 2211, 3539, 5871, 5949, 6954, 8309, 10896, 12771, 22382, 35112, 38267, 69866, 121229, 125754, 133979

Offset: 1

Author

Robert Price, Aug 15 2017

Keywords

• nonn
• more
• hard

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 8 followed by the digits 23 is prime (see Example section).

a(27) > 2*10^5.

Examples

			5 is in this sequence because (35*10^5 - 593)/9 = 388823 is prime.
Initial terms and associated primes:
a(1) = 3, 3823;
a(2) = 5, 388823;
a(3) = 6, 3888823;
a(4) = 14; 388888888888823;
a(5) = 24, 3888888888888888888888823; etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 38w23.

Crossrefs

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

Programs

Mathematica

Select[Range[2, 100000], PrimeQ[(35*10^# - 593)/9] &]

PARI

isok(n) = ispseudoprime((35*10^n - 593)/9) \\ Altug Alkan, Aug 15 2017

Extensions

a(24)-a(26) from Robert Price, Jul 18 2018