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Numbers k such that (82*10^k + 449)/9 is prime.
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%I #41 Jun 02 2024 20:58:41

%S 0,3,5,6,18,21,27,36,84,95,179,492,776,1260,4304,5010,5196,7718,15315,

%T 20838,20940,24303,26789,72612,157319

%N Numbers k such that (82*10^k + 449)/9 is prime.

%C For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 1 followed by the digits 61 is prime (see Example section).

%C a(26) > 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 91w61</a>.

%e 5 is in this sequence because (82*10^5 + 449)/9 = 911161 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 59;

%e a(2) = 3, 9161;

%e a(3) = 5, 911161;

%e a(4) = 6, 9111161;

%e a(5) = 18, 9111111111111111161; etc.

%t Select[Range[0, 100000], PrimeQ[(82*10^# + 449)/9] &] (* Corrected by _Georg Fischer_, Jul 22 2019 *)

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Feb 22 2017

%E a(25) from _Robert Price_, Nov 09 2019