A271821 - OEIS

%I #17 May 02 2024 22:54:32

%S 3,4,5,6,10,23,30,33,64,189,207,213,463,547,1225,1795,3726,3947,4989,

%T 5226,9825,11489,12666,14512,19588,28795,29903,31889,71357

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

%C 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 a(31) > 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 16w19</a>.

%e 4 is in this sequence because (5*10^4-143)/3 = 16619 is prime.

%e Initial terms and associated primes:

%e a(1) = 3, 1619;

%e a(2) = 4, 16619;

%e a(3) = 5, 166619;

%e a(4) = 6, 1666619;

%e a(5) = 10, 16666666619, etc.

%t Select[Range[0, 100000], PrimeQ[(5*10^#-143)/3] &]

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((5*10^n-143)/3), print1(n, ", "))); \\ _Altug Alkan_, Apr 14 2016

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

%K nonn,more

%O 1,1

%A _Robert Price_, Apr 14 2016