A273542 Numbers k such that (238*10^k - 1)/3 is prime.

0, 2, 3, 4, 6, 10, 12, 38, 40, 47, 59, 76, 131, 154, 227, 404, 762, 782, 987, 993, 3449, 5692, 10086, 11630, 15135, 26384, 28233, 33179, 48352, 103210, 118265, 145276, 151979, 209715, 210712

Offset: 1

Author

Robert Price, May 24 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digits 79 followed by k occurrences of the digit 3 is prime (see Example section).

a(36) > 3*10^5.

Examples

			3 is in this sequence because (238*10^3-1)/3 = 79333 is prime.
Initial terms and associated primes:
a(1) = 0, 79;
a(2) = 2, 7933;
a(3) = 3, 79333;
a(4) = 4, 793333;
a(5) = 6, 79333333, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 793w.

Crossrefs

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

Programs

Magma

[n: n in [0..500] | IsPrime((238*10^n - 1) div 3)]; // Vincenzo Librandi, May 25 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(238*10^# - 1)/3] &]

PARI

is(n)=ispseudoprime(238*10^n\3) \\ Charles R Greathouse IV, Jun 08 2016

Extensions

a(30)-a(33) from Robert Price, Apr 01 2020

a(34)-a(35) from Robert Price, Oct 26 2023