A094552 Numbers n such that there are integers a < b with a^2+(a+1)^2+...+(n-1)^2 = (n+1)^2+(n+2)^2+...+b^2.

52, 100, 137, 513, 565, 1247, 8195, 13041, 18921, 35344, 40223, 65918, 68906, 121759, 132720, 213831, 215221, 235469, 265654, 506049, 520654, 585046, 598337, 817454, 993142, 1339560, 1579353, 2331619, 2843086, 3594812

Offset

1,1

Comments

A094550 generalized to squares. Note that equality is attained only for very long sums of squares.

a(31) > 4*10^6. [From Donovan Johnson, Apr 20 2010]

Links

Table of n, a(n) for n=1..30.

Example

52 is in this sequence because 7^2+8^2+...+51^2 = 53^2+54^2+...+65^2.

Mathematica

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

Crossrefs

Cf. A094550, A094551, A094553.

Sequence in context: A026067 A039475 A274338 * A236461 A044141 A044522

Adjacent sequences: A094549 A094550 A094551 * A094553 A094554 A094555

Keyword

nonn

Author

T. D. Noe, May 10 2004

Extensions

a(14)-a(30) from Donovan Johnson, Apr 20 2010

Status

approved