A075404 Smallest m > n such that Sum_{i=n..m} i^2 is a square, or 0 if no such m exists.

24, 0, 4, 0, 0, 0, 29, 0, 32, 0, 22908, 0, 108, 0, 111, 0, 39, 28, 0, 21, 116, 80, 0, 0, 48, 0, 59, 77, 0, 198, 0, 609, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 171, 0, 147, 0, 0, 3533, 0, 0, 2132, 0, 92, 0, 0, 0, 305, 282, 0, 116, 0, 0, 0, 0, 0, 194, 36554, 0, 99, 0, 0, 0, 0, 0, 0, 276, 0, 0, 0, 136, 0, 0, 0, 332, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Zak Seidov, Sep 13 2002

Keywords

• nonn

Comments

For a(1) see A000330.

The corresponding squares are in A075405, the numbers of terms in the sum = a(n)-n+1 are in A075406.

All terms were verified by solving elliptic curves. If a(n)>0, then there may be additional values of m that produce squares. See A184763 for more information.

Examples

			a(1) = 24 because 1^2+...+24^2 = 70^2, a(7) = 29 because 7^2+...+29^2 = 92^2.
		

References

• See A180442.

Crossrefs

Cf. A000330, A075405, A075406, A180442 (n such that a(n) > 0).

Programs

Mathematica

s[n_,k_]:=Module[{m=n+k-1},(m(m+1)(2m+1)-n(n-1)(2n-1))/6]; mx=40000; Table[k=2; While[k
				

Extensions

Corrected and extended by Lior Manor, Sep 19 2002

Corrected and edited by T. D. Noe, Jan 21 2011