This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A098089 #50 Aug 29 2024 23:33:54
%S A098089 0,2,66,86,90,102,386,624,7784,18536,113757,135879
%N A098089 Numbers k such that 7*R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C A098089 Also numbers k such that (7*10^k + 11)/9 is prime.
%C A098089 Although perhaps a degenerate case, A002275 defines R(0)=0. Thus zero belongs in this sequence since 7*0 + 2 = 2 is prime. - _Robert Price_, Oct 28 2014
%C A098089 a(11) > 10^5. - _Robert Price_, Nov 22 2014
%C A098089 a(13) > 2*10^5. - _Tyler Busby_, Feb 01 2023
%H A098089 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77779.htm#prime">Prime numbers of the form 77...779</a>.
%H A098089 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>
%F A098089 a(n) = A056693(n-1) + 1 for n>1.
%e A098089 If k = 2, we get (7*10^2 + 11)/9 = (700+11)/9 = 79, which is prime.
%t A098089 Do[ If[ PrimeQ[ 7(10^n - 1)/9 + 2], Print[n]], {n, 0, 5000}] (* _Robert G. Wilson v_, Oct 15 2004 *)
%t A098089 Do[ If[ PrimeQ[((7*10^n) + 11)/9], Print[n]], {n, 0, 8131}] (* _Robert G. Wilson v_, Sep 27 2004 *)
%t A098089 Select[Range[0, 700], PrimeQ[(7 10^# + 11) / 9] &] (* _Vincenzo Librandi_, Nov 22 2014 *)
%o A098089 (Magma) [n: n in [0..300] | IsPrime((7*10^n+11) div 9)]; // _Vincenzo Librandi_, Nov 22 2014
%Y A098089 Cf. A002275, A056693, A093404.
%K A098089 more,nonn,hard
%O A098089 1,2
%A A098089 Julien Peter Benney (jpbenney(AT)ftml.net), Sep 14 2004
%E A098089 a(9) from Kamada link by _Ray Chandler_, Dec 23 2010
%E A098089 a(1)=0 added and Mathematica programs adapted by _Robert Price_, Oct 28 2014
%E A098089 a(11)-a(12) from _Tyler Busby_, Feb 01 2023