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Numbers k such that (13*10^k - 73) / 3 is prime.
0

%I #15 Jun 08 2024 00:01:16

%S 1,2,5,9,12,14,36,61,79,96,121,126,131,149,175,204,359,404,533,782,

%T 1869,1950,2712,2915,66551

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

%C 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).

%C a(26) > 2*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 43w09</a>.

%e 5 is in this sequence because (13*10^5 - 73) / 3 = 433309 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 19;

%e a(2) = 2, 409;

%e a(3) = 5, 433309;

%e a(4) = 9, 4333333309;

%e a(5) = 12, 4333333333309; etc.

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

%o (PARI) is(n)=ispseudoprime((13*10^n - 73)/3) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Dec 07 2016