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%I #29 May 25 2024 15:38:40
%S 2,3,5,6,11,12,26,32,36,75,137,143,279,290,363,716,770,1377,1638,4470,
%T 5952,10526,15132,27054,81485
%N Numbers k such that (73*10^k + 107)/9 is prime.
%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 1 followed by the digits 23 is prime (see Example section).
%C a(26) > 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 81w23</a>.
%e 3 is in this sequence because (73*10^3+107)/9 = 8123 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 823;
%e a(2) = 3, 8123;
%e a(3) = 5, 811123;
%e a(4) = 6, 8111123;
%e a(5) = 11, 811111111123, etc.
%t Select[Range[0, 100000], PrimeQ[(73*10^#+107)/9] &]
%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((73*10^n+107)/9), print1(n, ", "))); \\ _Altug Alkan_, Aug 11 2016
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,1
%A _Robert Price_, Aug 11 2016
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