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

0,7

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

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 *)

Prog

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

Crossrefs

Sequence in context: A025894 A339087 A051127 * A092606 A275948 A356325

Adjacent sequences: A070173 A070174 A070175 * A070177 A070178 A070179

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, May 13 2002

Extensions

More terms from Jason Earls, Jun 15 2002

Status

approved