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%I #16 May 02 2024 22:55:07
%S 1,2,5,7,13,16,17,25,44,52,197,233,241,389,838,856,2252,2945,5207,
%T 8020,10708,14663,16885,20366,20450,24121,24437,29348,134939
%N Numbers k such that (73*10^k + 143)/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 27 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 81w27</a>.
%e 5 is in this sequence because (73*10^5 + 143)/9 = 811127 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 97;
%e a(2) = 2, 827;;
%e a(3) = 5, 811127;
%e a(4) = 7, 81111127;
%e a(5) = 13, 81111111111127, etc.
%t Select[Range[0, 100000], PrimeQ[(73*10^# + 143)/9] &]
%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((73*10^n + 143)/9), print1(n, ", "))); \\ _Altug Alkan_, Apr 22 2016
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Apr 22 2016
%E a(29) from _Robert Price_, Jul 31 2019