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A294637 Numbers k such that (29*10^k - 113)/3 is prime. 0

%I #10 Oct 03 2019 15:04:07

%S 1,2,3,11,27,43,122,135,218,230,997,1005,1073,1133,1159,1541,2287,

%T 2912,3692,12503,45761,73659,125021

%N Numbers k such that (29*10^k - 113)/3 is prime.

%C For k>1, numbers such that the digit 9 followed by k-2 occurrences of the digit 6 followed by the digits 29 is prime (see Example section).

%C a(24) > 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/primedifficulty.txt">Search for 96w29</a>.

%e 2 is in this sequence because (29*10^2 - 113)/3 = 929 is prime.

%e Initial terms and primes associated:

%e a(1) = 1, 59;

%e a(2) = 2, 929;

%e a(3) = 3, 9629;

%e a(4) = 11, 966666666629;

%e a(5) = 27, 9666666666666666666666666629; etc.

%t Select[Range[1, 100000], PrimeQ[(29*10^# - 113)/3] &]

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 05 2017

%E a(23) from _Robert Price_, Oct 03 2019

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