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Numbers k such that (178*10^k - 7)/9 is prime.
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%I #14 May 25 2024 13:54:26

%S 0,1,3,7,12,13,21,40,67,69,132,213,259,1056,1639,1653,2913,6183,7086,

%T 8466,27475,55390

%N Numbers k such that (178*10^k - 7)/9 is prime.

%C Numbers k such that the digits 19 followed by k occurrences of the digit 7 is prime (see Example section).

%C a(23) > 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 197w</a>.

%e 3 is in this sequence because (178*10^3 - 7)/9 = 19777 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 19;

%e a(2) = 1, 197;

%e a(3) = 3, 19777;

%e a(4) = 7; 197777777;

%e a(5) = 12, 19777777777777; etc.

%t Select[Range[0, 100000], PrimeQ[(178*10^# - 7)/9] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Aug 14 2017