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Numbers k such that (7*10^k + 53)/3 is prime.
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%I #13 May 25 2024 19:37:56

%S 1,2,3,7,20,28,32,35,48,193,332,359,444,568,763,1414,10964,13703,

%T 15420,27384,49404,62362,65064,104113,187645

%N Numbers k such that (7*10^k + 53)/3 is prime.

%C For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 51 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 23w51</a>.

%e 2 is in this sequence because (7*10^2 + 53)/3 = 251 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 41;

%e a(2) = 2, 251;

%e a(3) = 3, 2351;

%e a(4) = 7, 23333351;

%e a(5) = 20, 233333333333333333351; etc.

%t Select[Range[0, 100000], PrimeQ[(7*10^# + 53)/3] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Oct 14 2017

%E a(24)-a(25) from _Robert Price_, May 20 2018