A070176 Let s(n) be smallest number >= n which is a sum of two squares (A001481); sequence gives s(n) - n.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, May 13 2002

Keywords

• nonn
• easy
• nice

Comments

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

a(A001481(n)) = 0; a(A022544(n)) > 0. [Reinhard Zumkeller, Feb 04 2012]

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000

Programs

Haskell

a070176 n = (head $ dropWhile (< n) a001481_list) - n
a070176_list = map a070176 [0..]
-- Reinhard Zumkeller, Feb 04 2012

Mathematica

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

Extensions

More terms from Jason Earls, Jun 15 2002