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%I #13 May 11 2024 19:36:34
%S 1,2,5,11,23,38,59,77,79,413,919,1079,1343,3194,5168,6266,12710,18711,
%T 47185,82347,170901,180710
%N Numbers k such that (79*10^k - 1)/3 is prime.
%C For k > 1, numbers k such that the digits 26 followed by k occurrences of the digit 3 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 263w</a>.
%e 2 is in this sequence because (79*10^2 - 1)/3 = 2633 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 263;
%e a(2) = 2, 2633;
%e a(3) = 5, 2633333;
%e a(4) = 11, 2633333333333;
%e a(5) = 23, 2633333333333333333333333; etc.
%t Select[Range[0, 100000], PrimeQ[(79*10^# - 1)/3] &]
%o (PARI) isok(k) = isprime((79*10^k - 1)/3); \\ _Michel Marcus_, Nov 12 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,2
%A _Robert Price_, Nov 11 2017
%E a(21)-a(22) from _Robert Price_, Jan 31 2020