A094523 Numbers n not of the form i^2+(i+1)^2 such that there are integers a < b with a^2+(a+1)^2+...+(n-1)^2 = n^2+(n+1)^2+...+b^2.

35, 39, 51, 111, 143, 160, 856, 2251, 2471, 2611, 3031, 3840, 3893, 4291, 5223, 5385, 5730, 7490, 7828, 9488, 21576, 27650, 30396, 31683, 38936, 41580, 48793, 56871, 60456, 64240, 64805, 66115, 85485, 90013

Offset

1,1

Comments

When n=i^2+(i+1)^2, then a=n-i-1 and b=n+i-1 is a solution. See A094553.

Links

Table of n, a(n) for n=1..34.

Example

35 is in this sequence because 18^2+19^2+...+34^2 = 35^2+36^2+...+42^2 and 35 is not the sum of two consecutive squares.

Mathematica

lst={}; Do[i1=n-1; i2=n; s1=i1^2; s2=i2^2; While[i1>1 && s1!=s2, If[s1<s2, i1--; s1=s1+i1^2, i2++; s2=s2+i2^2]]; m=(i2-i1)/2; m=m^2+(m+1)^2; If[s1==s2 && n!=m, AppendTo[lst, n]], {n, 2, 100000}]; lst

Crossrefs

Cf. A001844 (sum of two consecutive squares), A094553.

Sequence in context: A114965 A279410 A061755 * A249429 A249423 A219799

Adjacent sequences: A094520 A094521 A094522 * A094524 A094525 A094526

Keyword

nonn

Author

T. D. Noe, May 10 2004

Status

approved