A102945 - OEIS

%I #25 Sep 08 2022 08:45:16

%S 1,3,12,267,843,6300,37992,54117,121242,121621

%N Numbers k such that 10^k + 8*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (17*10^k + 1)/9 is prime.

%C No more terms below 133000. - _Serge Batalov_, May 15 2010

%C a(11) > 2*10^5. - _Robert Price_, Nov 16 2014

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/18889.htm#prime">Prime numbers of the form 188...889</a>.

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

%F a(n) = A102031(n) + 1.

%p A102945:=n->`if`(isprime((17*10^n+1)/9), n, NULL): seq(A102945(n), n=1..10^3); # _Wesley Ivan Hurt_, Nov 16 2014

%t Do[ If[ PrimeQ[(17*10^n + 1)/9], Print[n]], {n, 0, 10000}]

%t Select[Range[1000], PrimeQ[(17 10^# + 1) / 9] &] (* _Vincenzo Librandi_, Nov 17 2014 *)

%o (Magma) [n: n in [0..300] | IsPrime((17*10^n+1) div 9)]; // _Vincenzo Librandi_, Nov 17 2014

%Y Cf. A002275, A102031.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Dec 16 2004

%E More PRP terms a(7)-a(10). Sieved with srsieve and tested with Prime95 by _Serge Batalov_, May 15 2010