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Numbers k such that 7*R_k - 30 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
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%I #19 Apr 20 2024 02:46:22

%S 2,5,8,13,17,50,169,193,407,1496,1718,3610,6527,6889,12665,15949,

%T 23498,32969,44773,110027

%N Numbers k such that 7*R_k - 30 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also, numbers k such that (7*10^k - 277)/9 is prime.

%C Terms from Kamada.

%C a(21) > 200000. - _Tyler Busby_, Apr 20 2024

%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/7/77747.htm#prime">Prime numbers of the form 77...7747</a>.

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

%e For k=5, 7*R_5 - 30 = 77777 - 30 = 77747 which is prime.

%t Select[Range[0, 250000], PrimeQ[(7*10^# - 277)/9] &]

%o (Magma) [n: n in [2..500] | IsPrime((7*10^n-277) div 9)]; // _Vincenzo Librandi_, Apr 11 2015

%Y Cf. A002275.

%K more,hard,nonn

%O 1,1

%A _Robert Price_, Apr 10 2015

%E a(19)-a(20) from Kamada data by _Tyler Busby_, Apr 20 2024