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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