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Numbers k such that 9*10^k + 19 is prime.
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%I #23 May 02 2024 04:24:07

%S 1,2,4,5,10,14,25,34,40,63,74,129,149,345,370,425,477,627,951,1610,

%T 2564,2689,4227,7300,7444,8360,16541,21187,25685,31803,89858,92821

%N Numbers k such that 9*10^k + 19 is prime.

%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 0 followed by the digits 19 is prime (see Example section).

%C a(33) > 3*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 90w19</a>.

%e 4 is in this sequence because 9*10^4+19 = 90019 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 109;

%e a(2) = 2, 919;

%e a(3) = 4, 90019;

%e a(4) = 5, 900019;

%e a(5) = 10, 90000000019, etc.

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

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

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

%K nonn,more

%O 1,2

%A _Robert Price_, May 03 2016