login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k such that 3*R_k - 20 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
0

%I #16 Sep 08 2022 08:46:11

%S 2,3,4,7,9,37,39,67,73,183,216,1161,2622,2775,6240,22078,30384,189385

%N Numbers k such that 3*R_k - 20 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also, numbers k such that (10^k - 61)/3 is prime.

%C Terms from Kamada data.

%C a(19) > 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/3/33313.htm#prime">Prime numbers of the form 33...3313</a>.

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

%e For k=3, 3*R_3 - 20 = 333 - 20 = 313 which is prime.

%t Select[Range[0, 250000], PrimeQ[(10^# - 61)/3] &]

%o (Magma) [n: n in [2..300] | IsPrime((10^n-61) div 3)]; // _Vincenzo Librandi_, Apr 10 2015

%Y Cf. A002275.

%K nonn,more,hard

%O 1,1

%A _Robert Price_, Apr 09 2015