A214125 -id:A214125 - cp's OEIS frontend

A214123 Smallest positive k such that n+k(n-1) is prime.

1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 2, 3, 1, 1, 5, 5, 1, 9, 1, 1, 2, 1, 2, 3, 1, 3, 3, 1, 1, 9, 2, 1, 2, 1, 1, 3, 4, 1, 5, 1, 2, 3, 1, 3, 2, 5, 1, 3, 1, 1, 2, 1, 1, 5, 1, 3, 3, 11, 2, 5, 4, 1, 2, 1, 2, 3, 1, 1, 2, 7, 5, 3, 1, 1, 2, 5, 1, 3, 2, 1, 8, 1, 3, 11, 1, 3, 3, 1, 1, 5, 2, 3, 2, 1, 1, 3, 1, 1, 3, 5, 2, 5, 2, 1, 6, 5, 3, 9, 2, 1, 2, 1, 1, 3, 1, 7, 5, 1, 1, 5, 2, 5, 2, 1, 2, 3, 1, 7, 3, 1, 2, 11, 1, 1, 2, 5, 1, 3, 1, 1, 3, 5, 2, 9, 1, 5, 3

Offset: 2

Carl R. White, Jul 04 2012

Given n fenceposts, what is the minimum (but greater than zero) number of new posts which can be inserted between each consecutive pair of original posts to obtain a prime number of total posts?
Where the minimum is allowed to be zero, substitute a(n) = 0 for prime n.
a(n) is 1 when 2n-1 is prime, which is equivalent to a((p+1)/2)=1 for prime p > 2, therefore there are an infinite number of pairs of consecutive 1s in the sequence if the twin prime conjecture is true.

			For n = 5, we have fenceposts like so: ||||| . To insert 1 post between each pair of original posts would leave us with 9 posts: |;|;|;|;|, which is not prime. Inserting two: |;;|;;|;;|;;| gives 13 posts. This is prime so a(5) = 2.

Carl R. White, Table of n, a(n) for n = 2..10000

Cf. A214124, A214125

spk[n_]:=Module[{k=1},While[!PrimeQ[n+k(n-1)],k++];k]; Array[spk,150,2] (* Harvey P. Dale, May 04 2013 *)

A214124 Indices of consecutive maxima in A214123.

Original entry on oeis.org

2, 5, 8, 17, 20, 60, 160, 228, 318, 362, 522, 1638, 1692, 1998, 2054, 3834, 5208, 21210, 62810, 152352, 170168, 424784

Offset: 1

Carl R. White, Jul 04 2012

n where A214123(n) has a larger value than any previous value in that sequence, the corresponding values can be found in A214125.

It appears that for the n in this sequence, A214123(n) is O(log^2(n)).

Cf. A214123, A214125.

cp's OEIS Frontend

A214123 Smallest positive k such that n+k(n-1) is prime.

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