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%I #16 May 05 2024 00:21:04
%S 2,6,14,17,27,86,104,107,132,300,374,405,497,1179,1994,4274,5252,
%T 17939,39534,82898,85017,106083
%N Numbers k such that (182*10^k + 43)/9 is prime.
%C For k > 1, numbers k such that the digits 20 followed by k-1 occurrences of the digit 2 followed by the digit 7 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 202w7</a>.
%e 2 is in this sequence because (182*10^2 + 43)/9 = 2027 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 2027;
%e a(2) = 6, 20222227;
%e a(3) = 14, 2022222222222227;
%e a(4) = 17, 2022222222222222227;
%e a(5) = 27, 20222222222222222222222222227; etc.
%t Select[Range[0, 100000], PrimeQ[(182*10^# + 43)/9] &]
%o (PARI) isok(k) = isprime((182*10^k + 43)/9); \\ _Michel Marcus_, Nov 20 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Nov 19 2017
%E a(22) from _Robert Price_, Feb 01 2020