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A075404
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Smallest m > n such that Sum_{i=n..m} i^2 is a square, or 0 if no such m exists.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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REFERENCES
| See A180442.
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EXAMPLE
| a(1) = 24 because 1^2+...+24^2 = 70^2, a(7) = 29 because 7^2+...+29^2 = 92^2.
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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}]
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CROSSREFS
| Cf. A000330, A075405, A075406, A180442 (n such that a(n) > 0).
Sequence in context: A023923 A202184 A075406 * A194894 A128379 A111983
Adjacent sequences: A075401 A075402 A075403 * A075405 A075406 A075407
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Sep 13 2002
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EXTENSIONS
| Corrected and extended by Lior Manor (lior.manor(AT)gmail.com) Sep 19 2002
Corrected and edited by T. D. Noe (noe(AT)sspectra.com), Jan 21 2011
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