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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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

Crossrefs

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

Cf. A132470.

Programs

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 *)

Formula

a(n) = A051652(2*n). - Sean A. Irvine, Oct 01 2021

Extensions

More terms from James Sellers, Dec 07 1999

More terms from Amiram Eldar, Aug 28 2021