A051728 Smallest number at distance 2n from nearest prime.

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

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

Table of n, a(n) for n=0..37.

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

Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.

Cf. A132470.

Sequence in context: A106708 A138551 A133490 * A201954 A005359 A008842

Adjacent sequences: A051725 A051726 A051727 * A051729 A051730 A051731

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from James Sellers, Dec 07 1999

More terms from Amiram Eldar, Aug 28 2021

Status

approved