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Numbers k such that (49*10^k + 383)/9 is prime.
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%I #11 Jun 09 2024 18:05:18

%S 1,2,5,10,19,43,64,71,127,181,370,373,742,1085,1171,1438,2038,2269,

%T 2819,4802,7742,12010,47120,55129,139442,186409

%N Numbers k such that (49*10^k + 383)/9 is prime.

%C For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 4 followed by the digits 87 is prime (see Example section).

%C a(27) > 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 54w87</a>.

%e 4 is in this sequence because (49*10^5 + 383)/9 = 544487 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 97;

%e a(2) = 2, 587;

%e a(3) = 5, 544487;

%e a(4) = 10, 54444444487;

%e a(5) = 19, 54444444444444444487; etc.

%t Select[Range[0, 100000], PrimeQ[(49*10^# + 383)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Apr 21 2017

%E a(25)-a(26) from _Robert Price_, Apr 18 2019