A056685 - OEIS

%I #34 Sep 08 2022 08:45:01

%S 0,1,7,25,65,73,232,472,539,2773,64714

%N Numbers k such that 50*R_k + 3 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (5*10^(k+1)-23)/9 is prime.

%C a(12) > 10^5. - _Robert Price_, Nov 13 2014

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/5/55553.htm#prime">Prime numbers of the form 55...553</a>.

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

%F a(n) = A099416(n) - 1. - _Robert Price_, Nov 13 2014 [adapted by _Georg Fischer_, Jan 04 2021]

%t Do[ If[ PrimeQ[50*(10^n - 1)/9 + 3], Print[n]], {n, 0, 5000}]

%t Select[Range[0, 3000], PrimeQ[(5 10^(# + 1) - 23) / 9] &] (* _Vincenzo Librandi_, Nov 14 2014 *)

%o (Magma) [n: n in [0..400]| IsPrime((5*10^(n+1)-23)div 9)]; // _Vincenzo Librandi_, Nov 14 2014

%Y Cf. A002275, A099416.

%K hard,nonn

%O 1,3

%A _Robert G. Wilson v_, Aug 10 2000

%E a(11) derived from A099416 by _Robert Price_, Nov 13 2014