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Numbers k such that (536*10^k - 23)/9 is prime.
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%I #13 May 18 2024 11:31:46

%S 1,2,5,7,8,11,17,61,73,89,197,233,308,2096,3170,8003,15014,16166,

%T 26021,55748,102533,171601

%N Numbers k such that (536*10^k - 23)/9 is prime.

%C For k>1, numbers k such that the digits 59 followed by k-1 occurrences of the digit 5 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 595w3</a>.

%e 2 is in this sequence because (536*10^2 - 23)/9 = 5953 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 593;

%e a(2) = 2, 5953;

%e a(3) = 5, 5955553;

%e a(4) = 7, 595555553;

%e a(5) = 8, 5955555553; etc.

%t Select[Range[0, 100000], PrimeQ[(536*10^# - 23)/9] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 05 2017

%E a(21)-a(22) from _Robert Price_, Feb 23 2020