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A271821 Numbers k such that (5*10^k - 143)/3 is prime.

%I A271821 #17 May 02 2024 22:54:32
%S A271821 3,4,5,6,10,23,30,33,64,189,207,213,463,547,1225,1795,3726,3947,4989,
%T A271821 5226,9825,11489,12666,14512,19588,28795,29903,31889,71357
%N A271821 Numbers k such that (5*10^k - 143)/3 is prime.
%C A271821 For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 19 is prime (see Example section).
%C A271821 a(31) > 2*10^5.
%H A271821 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A271821 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 16w19</a>.
%e A271821 4 is in this sequence because (5*10^4-143)/3 = 16619 is prime.
%e A271821 Initial terms and associated primes:
%e A271821 a(1) = 3, 1619;
%e A271821 a(2) = 4, 16619;
%e A271821 a(3) = 5, 166619;
%e A271821 a(4) = 6, 1666619;
%e A271821 a(5) = 10, 16666666619, etc.
%t A271821 Select[Range[0, 100000], PrimeQ[(5*10^#-143)/3] &]
%o A271821 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((5*10^n-143)/3), print1(n, ", "))); \\ _Altug Alkan_, Apr 14 2016
%Y A271821 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A271821 nonn,more
%O A271821 1,1
%A A271821 _Robert Price_, Apr 14 2016