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%I #18 May 25 2024 15:39:04
%S 1,2,5,6,40,47,49,58,67,142,170,173,232,530,539,559,1651,1858,2695,
%T 6257,6714,8854,15066,15091,16890,51366,85249,135906
%N Numbers k such that (25*10^k - 73) / 3 is prime.
%C For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 09 is prime (see Example section).
%C a(29) > 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 83w09</a>.
%e 2 is in this sequence because (25*10^2 - 73) / 3 = 809 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 59;
%e a(2) = 2, 809;
%e a(3) = 5, 833309;
%e a(4) = 6, 8333309;
%e a(5) = 40, 83333333333333333333333333333333333333309, etc.
%t Select[Range[0, 100000], PrimeQ[(25*10^# - 73) / 3] &]
%o (PARI) is(n) = ispseudoprime((25*10^n - 73) / 3); \\ _Altug Alkan_, Sep 20 2016
%o (Magma) [n: n in [0..500] | IsPrime((25*10^n - 73) div 3)]; // _Vincenzo Librandi_, Sep 22 2016
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Sep 20 2016
%E a(28) from _Robert Price_, Sep 22 2019
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