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A051728
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Smallest number at distance 2n from nearest prime.
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21
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2, 0, 23, 53, 409, 293, 211, 1341, 1343, 2179, 3967, 15705, 16033, 19635, 31425, 24281, 31429, 31431, 31433, 155959, 38501, 58831, 203713, 268343, 206699, 370311, 370313, 370315, 370317, 1349591, 1357261, 1272749, 1357265, 1357267, 2010801, 2010803, 2010805, 2010807
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OFFSET
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0,1
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COMMENTS
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a(0) = 2. For n > 0, let f(m) = minimal distance from m to closest prime (excluding m itself). The a(n) = min { m : f(m) = 2n }.
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LINKS
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FORMULA
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MAPLE
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A051700 := proc(m) if m <= 2 then op(m+1, [2, 1, 1]) ; else min(nextprime(m)-m, m-prevprime(m)) ; fi ; end: A051728 := proc(n) local m ; if n = 0 then RETURN(2); else for m from 0 do if A051700(m) = 2 * n then RETURN(m) ; fi ; od: fi ; end: seq(A051728(n), n=0..20) ; # R. J. Mathar, Nov 18 2007
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MATHEMATICA
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a[n_] := Module[{m}, If[n == 0, Return[2], For[m = 0, True, m++, If[Min[NextPrime[m]-m, m-NextPrime[m, -1]] == 2*n, Return[m]]]]]; Table[Print[an = a[n]]; an, {n, 0, 33}] (* Jean-François Alcover, Feb 11 2014, after R. J. Mathar *)
Join[{2}, With[{t=Table[{n, Min[n-NextPrime[n, -1], NextPrime[n]-n]}, {n, 0, 1358000}]}, Table[SelectFirst[t, #[[2]]==2k&], {k, 33}]][[All, 1]]] (* Harvey P. Dale, Aug 13 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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