A099415 - OEIS

%I #26 Sep 08 2022 08:45:15

%S 12,13,609

%N Numbers k such that 5*R_k - 4 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (5*10^k - 41)/9 is prime.

%C a(4) > 10^5. - _Robert Price_, Nov 16 2014

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/5/55551.htm#prime">Prime numbers of the form 55...551</a>.

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

%F a(n) = A056684(n) + 1. - _Robert Price_, Nov 17 2014

%p A099415:=n->`if`(isprime((5*10^n-41)/9), n, NULL): seq(A099415(n), n=1..10^3); # _Wesley Ivan Hurt_, Nov 16 2014

%t Do[ If[ PrimeQ[ 5(10^n - 1)/9 - 4], Print[n]], {n, 15000}]

%t Select[Range[10000], PrimeQ[(5 10^# - 41) / 9] &] (* _Vincenzo Librandi_, Nov 17 2014 *)

%o (Magma) [n: n in [0..500] | IsPrime((5*10^n-41) div 9)]; // _Vincenzo Librandi_, Nov 17 2014

%Y Cf. A002275, A056684.

%K nonn,bref,more

%O 1,1

%A _Robert G. Wilson v_, Oct 14 2004