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Numbers k such that (34*10^k - 403)/9 is prime.
0

%I #11 May 25 2024 16:57:47

%S 3,24,39,58,268,324,346,354,412,478,681,802,1414,1662,2103,3994,7074,

%T 7323,21156,75387

%N Numbers k such that (34*10^k - 403)/9 is prime.

%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 7 followed by the digits 33 is prime (see Example section).

%C a(21) > 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 37w33</a>.

%e 3 is in this sequence because (34*10^3 - 403)/9 = 3733 is prime.

%e Initial terms and associated primes:

%e a(1) = 3, 3733;

%e a(2) = 24, 3777777777777777777777733;

%e a(3) = 39, 3777777777777777777777777777777777777733;

%e a(4) = 58, 37777777777777777777777777777777777777777777777777777777733; etc.

%t Select[Range[2, 100000], PrimeQ[(34*10^# - 403)/9] &]

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Oct 12 2017