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Numbers k such that (19*10^k + 161)/9 is prime.
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%I #13 May 02 2024 04:25:25

%S 2,3,5,6,8,18,36,59,80,162,197,200,405,432,930,1065,1496,1716,3213,

%T 5712,6303,7466,14150,23685,54608,59766

%N Numbers k such that (19*10^k + 161)/9 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 1 followed by the digits 29 is prime (see Example section).

%C a(27) > 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 21w29</a>.

%e 5 is in this sequence because (19*10^5 + 161)/9 = 211129 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 229;

%e a(2) = 3, 2129;

%e a(3) = 5, 211129;

%e a(4) = 6, 2111129;

%e a(5) = 8, 211111129, etc.

%t Select[Range[0, 100000], PrimeQ[(19*10^# + 161)/9] &]

%o (PARI) is(n)=ispseudoprime((19*10^n+161)/9) \\ _Charles R Greathouse IV_, Jun 13 2017

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

%K nonn,more

%O 1,1

%A _Robert Price_, Jul 23 2016