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 A097683 #36 Jan 17 2023 07:11:16
%S A097683 0,1,2,3,5,9,11,24,84,221,1314,2952,20016,51054
%N A097683 Numbers k such that R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C A097683 Also numbers k such that (10^k + 17)/9 is prime.
%C A097683 The corresponding values R_k + 2 are primes of the form "(n-1) ones followed by a three"; zero is a degenerate case. Related to the base-10 repunit primes.
%C A097683 a(15) > 10^5. - _Robert Price_, Oct 12 2014
%C A097683 By Kamada link, a(15) > 4*10^5. - _Jeppe Stig Nielsen_, Jan 17 2023
%H A097683 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11113.htm#prime">Prime numbers of the form 11...113</a>.
%H A097683 Henri Lifchitz and Renaud Lifchitz, PRP Top, <a href="http://www.primenumbers.net/prptop/searchform.php?form=%2810%5Ek%2B17%29%2F9">Search output for (10^k+17)/9</a>
%H A097683 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>
%F A097683 a(n) = A056654(n-1) + 1.
%e A097683 11113 = ((10^5)+17)/9 and 11113 is prime.
%p A097683 A097683:=n->`if`((10^n+17 mod 9) = 0 and isprime(floor((10^n+17)/9)),n,NULL): seq(A097683(n), n=0..10^3); # _Wesley Ivan Hurt_, Oct 12 2014
%t A097683 Do[ If[ PrimeQ[(10^n - 1)/9 + 2], Print[n]], {n, 0, 5951}] (* _Robert G. Wilson v_, Oct 15 2004 *)
%Y A097683 Cf. A002275, A004023, A056654, A097684, A097685.
%K A097683 more,nonn
%O A097683 1,3
%A A097683 _Carl R. White_ and Julien Peter Benney (jpbenney(AT)ftml.net), Aug 19 2004
%E A097683 a(11)-a(12) from _Robert G. Wilson v_, Oct 15 2004
%E A097683 Edited by _N. J. A. Sloane_, Apr 02 2009, at the suggestion of _Farideh Firoozbakht_
%E A097683 a(13) from Kamada link by _Ray Chandler_, Dec 23 2010
%E A097683 a(14) from _Robert Price_, Oct 12 2014