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A051728 Smallest number at distance 2n from nearest prime. 21
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
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 }.
f(m) is tabulated in A051700. - R. J. Mathar, Nov 18 2007
LINKS
FORMULA
a(n) = A051652(2*n). - Sean A. Irvine, Oct 01 2021
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Cf. A132470.
Sequence in context: A106708 A138551 A133490 * A201954 A005359 A008842
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Dec 07 1999
More terms from Amiram Eldar, Aug 28 2021
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)