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%I #15 May 03 2024 07:45:59
%S 1,2,5,8,32,37,38,53,104,128,241,866,872,943,1058,4351,16471,16925,
%T 23933,43511,73079,105811
%N Numbers k such that (5*10^k + 211)/9 is prime.
%C For k > 1, numbers k such that k-2 occurrences of the digit 5 followed by the digits 79 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 5w79</a>.
%e 2 is in this sequence because (5*10^2 + 211)/9 = 79 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 29;
%e a(2) = 2, 79;
%e a(3) = 5, 55579;
%e a(4) = 8, 55555579;
%e a(5) = 32, 55555555555555555555555555555579; etc.
%t Select[Range[0, 100000], PrimeQ[(5*10^# + 211)/9] &]
%o (PARI) isok(k) = isprime((5*10^k + 211)/9); \\ _Michel Marcus_, Dec 01 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 30 2017
%E a(22) from _Robert Price_, Feb 14 2018