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A102723 Smallest prime a(n) such that a(n)-x and a(n)+x, for x=1 to n, are all composite. 4
5, 23, 23, 53, 53, 211, 211, 211, 211, 211, 211, 1847, 1847, 2179, 2179, 2179, 2179, 3967, 3967, 16033, 16033, 16033, 16033, 24281, 24281, 24281, 24281, 24281, 24281, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 58831 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(2n+1)=a(2n). - Robert G. Wilson v, Feb 22 2005
Using Dirichlet's theorem, Sierpiński (1948) proved that a(n) exists for all n > 0. He noted that a(n) is a non-twin prime (A007510), except for a(1) = 5. - Jonathan Sondow, Oct 27 2017
LINKS
David A. Corneth, Table of n, a(n) for n = 1..479 (first 97 terms from Harvey P. Dale)
W. Sierpiński, Remarque sur la répartition des nombres premiers, Colloq. Math., 1 (1948), 193-194.
MATHEMATICA
f[n_] := Block[{k = 1}, While[ Union[ PrimeQ /@ Sort[ Flatten[ Table[{Prime[k] - i, Prime[k] + i}, {i, n}]]]] != {False}, k++ ]; Prime[k]]; Table[ f[n], {n, 40}] (* Robert G. Wilson v, Feb 22 2005 *)
cmpgap[n_]:=Module[{p=Prime[n]}, Min[p-NextPrime[p, -1], NextPrime[p]-p]]; Module[{nn=10000, prs}, prs=Table[{Prime[n], cmpgap[n]}, {n, nn}]; Table[ SelectFirst[ prs, #[[2]]>=k&], {k, 2, 50}]][[All, 1]] (* Harvey P. Dale, Oct 15 2021 *)
CROSSREFS
Sequence in context: A233756 A002582 A368425 * A136146 A289278 A167804
KEYWORD
nonn
AUTHOR
Ray G. Opao, Feb 06 2005
EXTENSIONS
a(12)-a(40) from Robert G. Wilson v, Feb 22 2005
STATUS
approved

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Last modified April 25 10:22 EDT 2024. Contains 371967 sequences. (Running on oeis4.)