A279171 Numbers k such that (13*10^k - 73) / 3 is prime.

1, 2, 5, 9, 12, 14, 36, 61, 79, 96, 121, 126, 131, 149, 175, 204, 359, 404, 533, 782, 1869, 1950, 2712, 2915, 66551

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 09 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 43w09.

Example

5 is in this sequence because (13*10^5 - 73) / 3 = 433309 is prime.
Initial terms and associated primes:
a(1) = 1, 19;
a(2) = 2, 409;
a(3) = 5, 433309;
a(4) = 9, 4333333309;
a(5) = 12, 4333333333309; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(13*10^# - 73) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((13*10^n - 73)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A287387 A371440 A287409 * A297465 A356089 A108165

Adjacent sequences: A279168 A279169 A279170 * A279172 A279173 A279174

Keyword

nonn,more,hard

Author

Robert Price, Dec 07 2016

Status

approved