%I #16 May 27 2024 07:16:50

%S 1,4,7,9,10,13,27,35,94,150,198,258,673,1194,1492,2320,2727,3767,6246,

%T 6877,14481,34327,57634,123137,190732

%N Numbers k such that (13*10^k - 61)/3 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 13 is prime (see Example section).

%C a(26) > 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 43w13</a>.

%e 4 is in this sequence because (13*10^4 - 61)/3 = 43313 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 23;

%e a(2) = 4, 43313;

%e a(3) = 7, 43333313;

%e a(4) = 9, 4333333313;

%e a(5) = 10, 43333333313; etc.

%t Select[Range[1, 100000], PrimeQ[(13*10^# - 61)/3] &]

%o (Magma) [n: n in [1..300] |IsPrime((13*10^n - 61) div 3)]; // _Vincenzo Librandi_, Aug 21 2017

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Aug 20 2017

%E a(24)-a(25) from _Robert Price_, Nov 28 2018