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%I #19 May 02 2024 04:27:55
%S 1,2,5,7,13,16,55,61,65,98,134,296,354,527,901,1206,1916,2899,3725,
%T 4709,7529,8942,12050,12880,15516,25976,62030,111020,195648,197941
%N Numbers k such that (29*10^k - 41)/3 is prime.
%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 6 followed by the digits 53 is prime (see Example section).
%C a(31) > 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 96w53</a>.
%e 5 is in this sequence because (29*10^5 - 41)/3 = 966653 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 83;
%e a(2) = 2, 953;
%e a(3) = 5, 966653;
%e a(4) = 7, 96666653;
%e a(5) = 13, 96666666666653, etc.
%t Select[Range[0, 100000], PrimeQ[(29*10^# - 41)/3] &]
%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime((29*10^n-41)/3), print1(n, ", "))); \\ _Altug Alkan_, Jul 21 2016
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Jul 21 2016
%E a(28)-a(30) from _Tyler Busby_, Mar 20 2024
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