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A273783 Numbers k such that (86*10^k - 77)/9 is prime.

%I A273783 #15 May 02 2024 04:24:51
%S A273783 2,3,8,9,12,14,27,32,50,80,98,99,194,237,338,828,830,1265,2583,3639,
%T A273783 5232,5940,9371,10268,13424,26975,36147,60165,69260,93263
%N A273783 Numbers k such that (86*10^k - 77)/9 is prime.
%C A273783 For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 5 followed by the digits 47 is prime (see Example section).
%C A273783 a(31) > 2*10^5.
%H A273783 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A273783 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 95w47</a>.
%e A273783 3 is in this sequence because (86*10^3 - 77)/9 = 9547 is prime.
%e A273783 Initial terms and associated primes:
%e A273783 a(1) = 2, 947;
%e A273783 a(2) = 3, 9547;
%e A273783 a(3) = 8, 955555547;
%e A273783 a(4) = 9, 9555555547;
%e A273783 a(5) = 12, 9555555555547, etc.
%t A273783 Select[Range[0, 100000], PrimeQ[(86*10^# - 77)/9] &]
%o A273783 (PARI) is(n)=ispseudoprime((86*10^n - 77)/9) \\ _Charles R Greathouse IV_, Jun 08 2016
%Y A273783 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A273783 nonn,more
%O A273783 1,1
%A A273783 _Robert Price_, May 30 2016