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Numbers k such that 41*10^k - 1 is prime.
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%I #12 May 18 2024 11:29:26

%S 1,2,4,6,17,19,36,60,70,83,92,276,324,330,486,3514,6062,10760,53958,

%T 58920,101892

%N Numbers k such that 41*10^k - 1 is prime.

%C For k > 1, numbers k such that the digits 40 followed by k occurrences of the digit 9 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 409w</a>.

%e 2 is in this sequence because 41*10^2 - 1 = 409 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 409;

%e a(2) = 2, 4099;

%e a(3) = 4, 409999;

%e a(4) = 6, 40999999;

%e a(5) = 17, 4099999999999999999; etc.

%t Select[Range[0, 100000], PrimeQ[41*10^# - 1] &]

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

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 10 2017

%E a(21) from _Robert Price_, Jan 31 2020