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%I #17 May 27 2024 07:17:02
%S 2,3,8,11,17,41,57,62,77,101,329,333,359,365,968,1169,1190,1772,2237,
%T 12075,30848,63200,190547
%N Numbers k such that (43*10^k + 83)/9 is prime.
%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 7 followed by the digits 87 is prime (see Example section).
%C a(24) > 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 47w87</a>.
%e 3 is in this sequence because (43*10^3 + 83)/9 = 4787 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 487;
%e a(2) = 3, 4787;
%e a(3) = 8, 477777787;
%e a(4) = 11, 477777777787;
%e a(5) = 17, 477777777777777787; etc.
%t Select[Range[0, 100000], PrimeQ[(43*10^# + 83)/9] &]
%o (Magma) [n: n in [1..300] |IsPrime((43*10^n + 83) div 9)]; // _Vincenzo Librandi_, Aug 21 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Aug 20 2017
%E a(23) from _Robert Price_, Nov 28 2018
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