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

1,1

Comments

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

Links

Table of n, a(n) for n=1..89.

Eric W. Weisstein, MathWorld: Linnik's Theorem

Wikipedia, Linnik's theorem.

Example

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

Mathematica

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

Crossrefs

Cf. A034693, A085420.

Sequence in context: A138904 A357138 A357180 * A342323 A374433 A135222

Adjacent sequences: A196657 A196658 A196659 * A196661 A196662 A196663

Keyword

nonn

Author

Frank M Jackson, Oct 05 2011

Status

approved