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 A075051 Smallest prime for which the n closest primes are smaller. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A249164 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

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Last modified April 14 20:07 EDT 2021. Contains 342962 sequences. (Running on oeis4.)