A070176 - OEIS

%I #22 Dec 15 2017 17:35:52

%S 0,0,0,1,0,0,2,1,0,0,0,2,1,0,2,1,0,0,0,1,0,4,3,2,1,0,0,2,1,0,2,1,0,1,

%T 0,1,0,0,2,1,0,0,3,2,1,0,3,2,1,0,0,1,0,0,4,3,2,1,0,2,1,0,2,1,0,0,2,1,

%U 0,3,2,1,0,0,0,5,4,3,2,1,0,0,0,2,1,0,3,2,1,0,0,6,5,4,3,2,1,0,0,1,0,0,2,1,0

%N Let s(n) be smallest number >= n which is a sum of two squares (A001481); sequence gives s(n) - n.

%C It is an unsolved problem to determine the rate of growth of this sequence.

%C a(A001481(n)) = 0; a(A022544(n)) > 0. [_Reinhard Zumkeller_, Feb 04 2012]

%D H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 208.

%H T. D. Noe, <a href="/A070176/b070176.txt">Table of n, a(n) for n = 0..10000</a>

%t sumOfTwoSquaresQ[n_] := With[{r = Ceiling[Sqrt[n]]}, Do[ Which[n == x^2 + y^2, Return[True], x == r && y == r, Return[False]], {x, 0, r}, {y, x, r}]]; a[n_] := For[s = n, True, s++, If[sumOfTwoSquaresQ[s], Return[s - n]]]; Table[a[n], {n, 0, 104}](* _Jean-François Alcover_, May 23 2012 *)

%t s2s[n_]:=Module[{i=0},While[SquaresR[2,n+i]==0,i++];i]; Array[s2s,110,0] (* _Harvey P. Dale_, Jun 16 2012 *)

%o (Haskell)

%o a070176 n = (head $ dropWhile (< n) a001481_list) - n

%o a070176_list = map a070176 [0..]

%o -- _Reinhard Zumkeller_, Feb 04 2012

%K nonn,easy,nice

%O 0,7

%A _N. J. A. Sloane_, May 13 2002

%E More terms from _Jason Earls_, Jun 15 2002