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%I #13 Jun 02 2024 14:04:53
%S 2,3,4,9,12,19,48,54,90,97,104,174,349,385,1020,1294,1737,2430,9040,
%T 14173,15604,17943,37447,149803,164043
%N Numbers k such that (2*10^k - 143)/3 is prime.
%C For k > 1, numbers k such that k-2 occurrences of the digit 6 followed by the digits 19 is prime (see Example section).
%C a(26) > 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 6w19</a>.
%e 3 is in this sequence because (2*10^3 - 143)/3 = 619 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 19;
%e a(2) = 3, 619;
%e a(3) = 4, 6619;
%e a(4) = 9, 666666619;
%e a(5) = 12, 666666666619; etc.
%t Select[Range[2, 100000], PrimeQ[(2*10^# - 143)/3] &]
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Feb 04 2017
%E a(24)-a(25) from _Robert Price_, Mar 14 2018