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%I #12 Sep 08 2022 08:46:19
%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 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/primedifficulty.txt">Search for 43w13.</a>
%e 4 is in this sequence because (13*10^4 - 61)/3 = 43313 is prime.
%e Initial terms and primes associated:
%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
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