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 A196660 #27 Mar 18 2025 16:20:32
%S A196660 2,1,1,1,3,1,1,2,1,1,3,1,7,2,1,1,3,2,1,2,1,1,5,1,5,3,1,2,5,1,1,3,3,1,
%T A196660 3,1,1,2,5,1,3,1,5,2,1,2,5,3,1,2,1,1,3,1,1,2,1,2,5,2,7,6,3,1,5,1,5,3,
%U A196660 1,1,3,4,13,5,1,1,3,2,1,2,7,1,3,1,5,2,1,2,15
%N A196660 Smallest k>0 such that k*n+(n-1) is prime.
%C A196660 Conjecture: for every n there exists k < n (apart from a(1)) such that k*n+(n-1) is prime. See A034693.
%H A196660 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LinniksTheorem.html">Linnik's Theorem</a>
%H A196660 Wikipedia, <a href="http://en.wikipedia.org/wiki/Linnik%27s_theorem">Linnik's theorem</a>.
%e A196660 If n=13, the smallest prime in the sequence 25,38,51,64,77,90,103,... is 103, so a(13)=7.
%t A196660 q[n_]:=(k=0; While[!PrimeQ[++k*n+n-1]]; k); Table[q[n],{n,1,100}]
%o A196660 (PARI) a(n) = my(k=1); while (!isprime(k*n+(n-1)), k++); k; \\ _Michel Marcus_, Mar 18 2025
%Y A196660 Cf. A034693, A085420.
%K A196660 nonn
%O A196660 1,1
%A A196660 _Frank M Jackson_, Oct 05 2011