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Numbers k such that R_k + 40 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #15 Sep 08 2022 08:46:11

%S 1,3,4,7,60,394,552,1164,1494,5398,7899,11254,13224,77637,118324,

%T 120574,142425,142699,157792,188164

%N Numbers k such that R_k + 40 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also, numbers k such that (10^k + 359)/9 is prime.

%C Terms from Kamada data. Note that Kamada does not recognize k=1 as 41 is a degenerate case of form AAA..ABA.

%C a(21) > 10^6.

%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/1/11151.htm#prime">Prime numbers of the form 11...1151</a>.

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

%e For k=3, R_3 + 40 = 111 + 40 = 151 which is prime.

%t Select[Range[0, 250000], PrimeQ[(10^# + 359)/9] &]

%o (Magma) [n: n in [1..400] | IsPrime((10^n+359) div 9)]; // _Vincenzo Librandi_, Apr 10 2015

%Y Cf. A002275.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Apr 09 2015