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Numbers k such that R_k + 50 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #19 Sep 08 2022 08:46:11

%S 2,5,8,18,38,1919,1934,4250,4397,12626,13151,26693,81353,83916

%N Numbers k such that R_k + 50 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also, numbers k such that (10^k + 449)/9 is prime.

%C Terms from Kamada data.

%C a(15) > 2.5*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/aaaba.htm">Near-repdigit numbers of the form AA...AABA</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11161.htm#prime">Prime numbers of the form 11...1161</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%e For k=5, R_5 + 50 = 11111 + 50 = 11161 which is prime.

%t Select[Range[0, 250000], PrimeQ[(10^# + 449)/9] &]

%o (Magma) [n: n in [1..400] | IsPrime((10^n+449) div 9)]; // _Vincenzo Librandi_, Apr 10 2015

%Y Cf. A002275.

%K more,hard,nonn

%O 1,1

%A _Robert Price_, Apr 09 2015