The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A075404 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#20 by Russ Cox at Fri Mar 30 17:35:31 EDT 2012

EXTENSIONS

Corrected and extended by _Lior Manor (lior.manor(AT)gmail.com) _ Sep 19 2002

Discussion

Fri Mar 30

17:35

OEIS Server: https://oeis.org/edit/global/167

#19 by Russ Cox at Fri Mar 30 17:26:03 EDT 2012

AUTHOR

_Zak Seidov (zakseidov(AT)yahoo.com), _, Sep 13 2002

Discussion

Fri Mar 30

17:26

OEIS Server: https://oeis.org/edit/global/139

#18 by Russ Cox at Fri Mar 30 17:22:26 EDT 2012

EXTENSIONS

Corrected and edited by _T. D. Noe (noe(AT)sspectra.com), _, Jan 21 2011

Discussion

Fri Mar 30

17:22

OEIS Server: https://oeis.org/edit/global/120

#17 by T. D. Noe at Fri Jan 21 16:34:01 EST 2011

STATUS

reviewed

approved

#16 by T. D. Noe at Fri Jan 21 16:25:59 EST 2011

STATUS

proposed

reviewed

#15 by T. D. Noe at Fri Jan 21 16:25:44 EST 2011

COMMENTS

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.

#14 by T. D. Noe at Fri Jan 21 15:44:29 EST 2011

NAME

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

STATUS

reviewed

proposed

#13 by T. D. Noe at Fri Jan 21 13:35:47 EST 2011

STATUS

proposed

reviewed

#12 by T. D. Noe at Fri Jan 21 13:32:15 EST 2011

COMMENTS

All terms were verified by solving elliptic curves.

EXAMPLE

a(1) = 24 because 1^2+...+24^2 = b(1)^2 = 70^2, a(2) = 0 because a(2) is not known, a(7) = 29 because 7^2+...+29^2 = b(7)^2 = 92^2. [What does "not known" mean? - N. J. A. Sloane (njas(AT)research.att.com)]

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, k=0, n+k-1], {n, 100}]

Discussion

Fri Jan 21

13:35

T. D. Noe: All done.

#11 by T. D. Noe at Fri Jan 21 13:06:10 EST 2011

DATA

24, 0, 2, 4, 0, 0, 0, 23, 29, 0, 24, 32, 0, 22898, 22908, 0, 96, 108, 0, 97, 111, 0, 23, 11, 39, 28, 0, 2, 96, 59, 21, 116, 80, 0, 0, 24, 48, 0, 33, 50, 59, 77, 0, 169, 198, 0, 578, 609, 0, 0, 0, 0, 0, 11, 48, 0, 0, 0, 0, 0, 24, 67, 0, 0, 0, 0, 0, 122, 171, 0, 96, 147, 0, 0, 3479, 3533, 0, 0, 2075, 2132, 0, 33, 92, 0, 0, 0, 242, 218, 305, 282, 0, 50, 116, 0, 0, 0, 0, 0, 122, 36481, 194, 36554, 0, 24, 99, 0, 0, 0, 0, 0, 0, 194, 276, 0, 0, 0, 50, 136, 0, 0, 0, 242, 332, 0, 0, 0, 0, 0, 0, 0, 0, 0

COMMENTS

Most of the large terms were wrong. Related to A180442, which is still being edited.

REFERENCES

See A180442.

MATHEMATICA

s[n_, k_]:=Module[{m=n+k-1}, (m(m+1)(2m+1)-n(n-1)(2n-1))/6]; mx=10^640000; Table[k=2; While[k<mx && !IntegerQ[Sqrt[s[n, k]]], k++]; If[k==mx, k=0]; , n+k, -1], {n, 100}]

CROSSREFS

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

EXTENSIONS

Corrected and edited by T. D. Noe (noe(AT)sspectra.com), Jan 21 2011