A075051 Smallest prime for which the n closest primes are smaller.

3, 113, 113, 113, 1327, 1327, 15683, 15683, 248909, 265621, 492113, 492113, 3851459, 7743233, 18640103, 18640103, 18640103, 435917249, 435917249, 435917249, 649580171, 649580171, 19187736221, 19187736221, 19187736221, 94746870541, 94746870541, 673420121333, 1975675658371

Offset

1,1

Comments

It is surprising that few of the above entries are at the beginning of a prime gap in A000230 or A002386.

Links

Table of n, a(n) for n=1..29.

Example

The smallest prime number for which the three closest primes to itself are all smaller than itself is 113 (the closest primes being 109, 107 and 103). So a(3)=113.

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; k = 1; Do[ps = Table[0, {n + 1}]; ps = Append[ps, Max[k, 1]]; While[ps = Drop[ps, 1]; ps = Append[ps, NextPrim[ ps[[ -1]]]]; ps[[ -1]] - ps[[ -2]] <= ps[[ -2]] - ps[[1]], ]; Print[ ps[[ -2]]]; k = PrevPrim[ ps[[1]]], {n, 1, 30}]

Crossrefs

Cf. A001223, A074979, A074982, A075030, A075037, A075038, A075043 & A075050.

Sequence in context: A199640 A221618 A300814 * A139929 A142603 A350053

Adjacent sequences: A075048 A075049 A075050 * A075052 A075053 A075054

Keyword

nonn

Author

Neil Fernandez, Oct 10 2002

Extensions

Edited and extended by Robert G. Wilson v, Oct 12 2002

a(23)-a(29) from Donovan Johnson, Jun 19 2008

Status

approved