%I #27 Sep 08 2022 08:45:16

%S 3,5,9,12,27,51,53,147,155,257,519,603,2885,9509,10524,19650,32508,

%T 79445,158909

%N Numbers n such that 3*10^n + 2*R_n + 7 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Also numbers n such that (29*10^n+61)/9 is prime.

%C a(19) > 10^5. - _Robert Price_, Apr 05 2015

%C a(20) > 2*10^5. - _Robert Price_, Aug 12 2018

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/3/32229.htm#prime">Prime numbers of the form 322...229</a>.

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

%F a(n) = A101831(n) + 1.

%t Do[ If[ PrimeQ[(29*10^n + 61)/9], Print[n]], {n, 0, 10000}]

%t Select[Range[10000], PrimeQ[(29 10^# + 61) / 9] &] (* _Vincenzo Librandi_, Apr 06 2015 *)

%o (Magma) [n: n in [0..500] | IsPrime((29*10^n + 61) div 9)]; // _Vincenzo Librandi_, Apr 06 2015

%Y Cf. A002275, A101831.

%K more,nonn

%O 1,1

%A _Robert G. Wilson v_, Dec 17 2004

%E A(13) from Julien Peter Benney (jpbenney(AT)ftml.net), Jan 16 2005

%E A(14) from _Robert G. Wilson v_, Jan 17 2005

%E Addition of a(15)-a(16) from Kamada data by _Robert Price_, Dec 12 2010

%E a(17) from Erik Branger May 01 2013 by _Ray Chandler_, Aug 16 2013

%E a(18) from _Robert Price_, Apr 05 2015

%E a(19) from _Robert Price_, Aug 12 2018