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

Author

Neil Fernandez, Oct 10 2002

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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}]

Extensions

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

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