login

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

Numbers n such that 3*10^n + 5*R_n - 4 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
1

%I #20 Sep 08 2022 08:45:16

%S 1,6,9,15,24,48,73,75,97,249,273,2488,14499,74773,87448

%N Numbers n such that 3*10^n + 5*R_n - 4 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (32*10^n-41)/9 is prime.

%C a(16) > 10^5. - _Robert Price_, May 24 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/35551.htm#prime">Prime numbers of the form 355...551</a>.

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

%F a(n) = A101835(n) + 1.

%t Do[ If[ PrimeQ[(32*10^n-41)/9], Print[n]], {n, 0, 10000}]

%t Select[Range[0, 10000], PrimeQ[(32 10^# - 41)/9] &] (* _Vincenzo Librandi_, May 25 2015 *)

%o (Magma) [n: n in [0..2000] | IsPrime((32*10^n-41) div 9)]; // _Vincenzo Librandi_, May 25 2015

%Y Cf. A002275, A101835.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 17 2004

%E Addition of a(13) from Kamada data by _Robert Price_, Dec 13 2010

%E a(14)-a(15) from _Robert Price_, May 24 2015