%I #27 May 18 2024 11:33:10
%S 1,3,5,6,9,13,120,220,568,640,666,1205,1600,2479,2482,2939,3077,8649,
%T 9520,12407,33421,36162,41190,65340
%N Numbers k such that (10^k + 47)/3 is prime.
%C For k > 1, numbers k such that k-2 occurrences of the digit 3 followed by the digits 49 is prime (see Example section). - _Robert Price_, Nov 10 2017
%C a(25) > 3*10^5. - _Robert Price_, Oct 26 2023
%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 3w49</a>.
%e 3 is in this sequence because (10^3 + 47)/3 = 349 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 19;
%e a(2) = 3, 349;
%e a(3) = 5, 33349;
%e a(4) = 6, 333349;
%e a(5) = 9, 333333349; etc.
%t Select[Range[0, 100000], PrimeQ[(10^# + 47)/3] &]
%o (Magma) [n: n in [0..500] |IsPrime((10^n+47) div 3)];
%o (PARI) is(n) = ispseudoprime((10^n + 47) / 3); \\ _Altug Alkan_, Sep 26 2016
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%Y See also similar sequences listed in A274986.
%K nonn,more,hard
%O 1,2
%A _Vincenzo Librandi_, Sep 26 2016
%E a(18)-a(24) from _Robert Price_, Nov 10 2017