A196660 - OEIS

%I #23 Feb 16 2025 08:33:15

%S 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 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 1,1,3,4,13,5,1,1,3,2,1,2,7,1,3,1,5,2,1,2,15

%N Smallest k>0 such that k*n+(n-1) is prime.

%C Conjecture: for every n their exists k < n (apart from a(1)) such that k*n+(n-1) is prime. See A034693.

%H Eric W. Weisstein, <a href="https://mathworld.wolfram.com/LinniksTheorem.html">MathWorld: Linnik's Theorem</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Linnik%27s_theorem">Linnik's theorem</a>.

%e If n=13, the smallest prime in the sequence 25,38,51,64,77,90,103,... is 103, so a(13)=7.

%t q[n_]:=(k=0; While[!PrimeQ[++k*n+n-1]]; k); Table[q[n],{n,1,100}]

%Y Cf. A034693, A085420.

%K nonn,changed

%O 1,1

%A _Frank M Jackson_, Oct 05 2011