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Numbers k such that (44*10^k - 719)/9 is prime.
0

%I #15 May 03 2024 07:45:42

%S 2,4,11,14,25,55,89,131,644,2938,3338,4265,5200,6178,7075,10379,12830,

%T 26377,42947,98284,121297

%N Numbers k such that (44*10^k - 719)/9 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 8 followed by the digits 09 is prime (see Example section).

%C a(22) > 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 48w09</a>.

%e 2 is in this sequence because (44*10^2 - 719)/9 = 409 is prime.

%e Initial terms and associated primes:

%e a(1) = 2, 409;

%e a(2) = 4, 48809;

%e a(3) = 11, 488888888809;

%e a(4) = 14, 488888888888809;

%e a(5) = 25, 48888888888888888888888809; etc.

%t Select[Range[2, 100000], PrimeQ[(44*10^# - 719)/9] &]

%o (PARI) isok(k) = isprime((44*10^k - 719)/9); \\ _Michel Marcus_, Dec 01 2017

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

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Nov 30 2017

%E a(21) from _Robert Price_, Dec 31 2018