A272537 Numbers k such that (28*10^k + 173)/3 is prime.

0, 1, 2, 3, 9, 11, 13, 15, 17, 24, 37, 44, 48, 58, 65, 104, 393, 413, 1265, 2292, 2620, 3037, 3628, 5159, 5629, 12809, 18572, 26875, 29695, 32267, 34277, 43621, 138768, 220800

Offset: 1

Author

Robert Price, May 02 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 91 is prime (see Example section).

a(35) > 3*10^5.

Examples

			3 is in this sequence because (28*10^3 + 173)/3 = 9391 is prime.
Initial terms and associated primes:
a(1) = 0, 67;
a(2) = 1, 151;
a(3) = 2, 991;
a(4) = 3, 9391;
a(5) = 9, 9333333391, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 93w91.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(28*10^# + 173)/3] &]

PARI

is(n)=ispseudoprime((28*10^n + 173)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(33) from Robert Price, Dec 25 2019

a(34) from Robert Price, Jul 02 2024