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Numbers k such that (202*10^k - 13)/9 is prime.
0

%I #12 May 03 2024 07:45:32

%S 1,2,4,20,22,34,35,41,185,547,644,713,1489,1885,3211,3257,3625,6733,

%T 47732,165569,172940,195383

%N Numbers k such that (202*10^k - 13)/9 is prime.

%C For k > 0, numbers k such that the digits 22 followed by k-1 occurrences of the digit 4 followed by the digit 3 is prime (see Example section).

%C a(23) > 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 224w3</a>.

%e 2 is in this sequence because (202*10^2 - 13)/9 = 2243 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 223;

%e a(2) = 2, 2243;

%e a(3) = 4, 224443;

%e a(4) = 20, 2244444444444444444443;

%e a(5) = 22, 224444444444444444444443; etc.

%t Select[Range[0, 100000], PrimeQ[(202*10^# - 13)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 28 2017

%E a(20)-a(22) from _Robert Price_, Jan 08 2020