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Numbers k such that (29*10^k + 259)/9 is prime.
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%I #13 Jun 08 2024 08:55:22

%S 1,3,4,6,9,10,24,27,66,76,136,346,399,978,1228,2227,4005,5916,6394,

%T 7438,18934,20020,31866,85438

%N Numbers k such that (29*10^k + 259)/9 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 2 followed by the digits 51 is prime (see Example section).

%C a(25) > 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 32w51</a>.

%e 3 is in this sequence because (29*10^3 + 259)/9 = 3251 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 61;

%e a(2) = 3, 3251;

%e a(3) = 4, 32251;

%e a(4) = 6, 3222251;

%e a(5) = 9, 3222222251; etc.

%t Select[Range[0, 100000], PrimeQ[(29*10^# + 259)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Apr 01 2017