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Numbers k such that (4*10^k + 83)/3 is prime.
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%I #12 Jun 08 2024 00:00:24

%S 0,1,3,7,9,15,17,27,37,55,58,155,228,480,720,1305,1573,2173,2547,2767,

%T 5448,5500,9468,14268,35207,58155,102612,114340,124420,169559

%N Numbers k such that (4*10^k + 83)/3 is prime.

%C For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 3 followed by the digits 61 is prime (see Example section).

%C a(31) > 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 13w61</a>.

%e 3 is in this sequence because (4*10^3 + 83) / 3 = 1361 is prime.

%e Initial terms and associated primes:

%e a(1) = 0, 29;

%e a(2) = 1, 41;

%e a(3) = 3, 1361;

%e a(4) = 7, 13333361;

%e a(5) = 9, 1333333361; etc.

%t Select[Range[0, 100000], PrimeQ[(4*10^# + 83) / 3] &]

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

%K nonn,more,hard

%O 1,3

%A _Robert Price_, Jan 09 2017

%E a(27)-a(30) from _Robert Price_, Feb 02 2018