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A075404
Smallest m > n such that Sum_{i=n..m} i^2 is a square, or 0 if no such m exists.
4
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
1,1
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.
REFERENCES
See A180442.
EXAMPLE
a(1) = 24 because 1^2+...+24^2 = 70^2, a(7) = 29 because 7^2+...+29^2 = 92^2.
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<mx && !IntegerQ[Sqrt[s[n, k]]], k++]; If[k==mx, 0, n+k-1], {n, 100}]
CROSSREFS
Cf. A000330, A075405, A075406, A180442 (n such that a(n) > 0).
Sequence in context: A376347 A376346 A075406 * A356304 A308234 A362795
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 13 2002
EXTENSIONS
Corrected and extended by Lior Manor Sep 19 2002
Corrected and edited by T. D. Noe, Jan 21 2011
STATUS
approved