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%I #17 May 03 2024 18:40:02
%S 2,5,9,11,23,27,33,111,119,314,375,551,1694,3413,3495,4172,9287,10412,
%T 179697
%N Numbers k such that (29*10^k + 223)/9 is prime.
%C For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 2 followed by the digits 47 is prime (see Example section).
%C a(20) > 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 32w47</a>.
%e 2 is in this sequence because (29*10^2 + 223)/9 = 347 is prime.
%e Initial terms and associated primes:
%e a(1) = 2, 347;
%e a(2) = 5, 322247;
%e a(3) = 9, 3222222247;
%e a(4) = 11, 322222222247;
%e a(5) = 23, 322222222222222222222247; etc.
%t Select[Range[0, 100000], PrimeQ[(29*10^# + 223)/9] &]
%o (PARI) isok(k) = isprime((29*10^k + 223)/9); \\ _Michel Marcus_, Nov 24 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more,hard
%O 1,1
%A _Robert Price_, Nov 24 2017
%E a(19) from _Robert Price_, Sep 08 2018
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