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Numbers k such that (86*10^k - 77)/9 is prime.
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%I #15 May 02 2024 04:24:51

%S 2,3,8,9,12,14,27,32,50,80,98,99,194,237,338,828,830,1265,2583,3639,

%T 5232,5940,9371,10268,13424,26975,36147,60165,69260,93263

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

%C 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 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 95w47</a>.

%e 3 is in this sequence because (86*10^3 - 77)/9 = 9547 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 947;

%e a(2) = 3, 9547;

%e a(3) = 8, 955555547;

%e a(4) = 9, 9555555547;

%e a(5) = 12, 9555555555547, etc.

%t Select[Range[0, 100000], PrimeQ[(86*10^# - 77)/9] &]

%o (PARI) is(n)=ispseudoprime((86*10^n - 77)/9) \\ _Charles R Greathouse IV_, Jun 08 2016

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more

%O 1,1

%A _Robert Price_, May 30 2016