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A275323 Numbers k such that (19*10^k + 161)/9 is prime.

%I A275323 #13 May 02 2024 04:25:25
%S A275323 2,3,5,6,8,18,36,59,80,162,197,200,405,432,930,1065,1496,1716,3213,
%T A275323 5712,6303,7466,14150,23685,54608,59766
%N A275323 Numbers k such that (19*10^k + 161)/9 is prime.
%C A275323 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 A275323 a(27) > 10^5.
%H A275323 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A275323 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 21w29</a>.
%e A275323 5 is in this sequence because (19*10^5 + 161)/9 = 211129 is prime.
%e A275323 Initial terms and associated primes:
%e A275323 a(1) = 2, 229;
%e A275323 a(2) = 3, 2129;
%e A275323 a(3) = 5, 211129;
%e A275323 a(4) = 6, 2111129;
%e A275323 a(5) = 8, 211111129, etc.
%t A275323 Select[Range[0, 100000], PrimeQ[(19*10^# + 161)/9] &]
%o A275323 (PARI) is(n)=ispseudoprime((19*10^n+161)/9) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A275323 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A275323 nonn,more
%O A275323 1,1
%A A275323 _Robert Price_, Jul 23 2016