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%I #13 Jun 02 2024 14:04:44
%S 3,7,10,15,28,35,70,183,243,298,366,388,607,791,827,1704,1732,1743,
%T 2755,2766,2983,3312,7173,16365,18234,102163,104461,136813,154078
%N Numbers k such that 4*10^k - 57 is prime.
%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 43 is prime (see Example section).
%C a(30) > 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 39w43</a>.
%e 3 is in this sequence because 4*10^3 - 57 = 3943 is prime.
%e Initial terms and associated primes:
%e a(1) = 3, 3943;
%e a(2) = 7, 39999943;
%e a(3) = 10, 39999999943;
%e a(4) = 15, 3999999999999943;
%e a(5) = 28, 39999999999999999999999999943; etc.
%t Select[Range[2, 100000], PrimeQ[4*10^# - 57] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Jan 25 2017
%E a(26)-a(29) from _Robert Price_, Oct 13 2018