A196660 Smallest k>0 such that k*n+(n-1) is prime.

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

Offset: 1

Author

Frank M Jackson, Oct 05 2011

Keywords

• nonn

Comments

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

Examples

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

Links

• Eric Weisstein's World of Mathematics, Linnik's Theorem
• Wikipedia, Linnik's theorem.

Crossrefs

Cf. A034693, A085420.

Programs

Mathematica

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

PARI

a(n) = my(k=1); while (!isprime(k*n+(n-1)), k++); k; \\ Michel Marcus, Mar 18 2025