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A196660 Smallest k>0 such that k*n+(n-1) is prime. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A317176 A318812 A138904 * A135222 A285706 A124094

Adjacent sequences:  A196657 A196658 A196659 * A196661 A196662 A196663

KEYWORD

nonn

AUTHOR

Frank M Jackson, Oct 05 2011

STATUS

approved

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Last modified March 26 06:48 EDT 2019. Contains 321481 sequences. (Running on oeis4.)