The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A003995

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A003995

Sum of (any number of) distinct squares: of form r^2 + s^2 + t^2 + ... with 0 <= r < s < t < ...
(history; published version)

#39 by Michael De Vlieger at Tue Jan 14 23:08:53 EST 2025

STATUS

reviewed

approved

#38 by Andrew Howroyd at Tue Jan 14 22:47:04 EST 2025

STATUS

proposed

reviewed

#37 by Mike Sheppard at Tue Jan 14 22:43:28 EST 2025

STATUS

editing

proposed

#36 by Mike Sheppard at Tue Jan 14 22:41:58 EST 2025

COMMENTS

The set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way (see ref)

REFERENCES

Montgomery, Hugh, and Ulrike Vorhauer. <a href="https://www.ams.org/journals/mcom/2004-73-245/S0025-5718-03-01513-8/S0025-5718-03-01513-8.pdf">"Greedy sums of distinct squares."</a> Mathematics of computation 73.245 (2004): 493-513.

STATUS

proposed

editing

Discussion

Tue Jan 14

22:43

Mike Sheppard: Reverting back the edits, as 'greedy sum of distinct squares' is a different sequence. 38 in this sequence, but not if 'greedy'.

#35 by Mike Sheppard at Tue Jan 14 22:28:19 EST 2025

STATUS

editing

proposed

#34 by Mike Sheppard at Tue Jan 14 22:26:45 EST 2025

COMMENTS

The set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way (see ref)

REFERENCES

STATUS

approved

editing

Discussion

Tue Jan 14

22:28

Mike Sheppard: Added link to reference and note about density

#33 by Charles R Greathouse IV at Sat Jun 13 00:48:08 EDT 2015

LINKS

<a href="/index/Rec#order_02">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (2,-1).

Discussion

Sat Jun 13

00:48

OEIS Server: https://oeis.org/edit/global/2439

#32 by N. J. A. Sloane at Wed Dec 24 13:15:11 EST 2014

STATUS

editing

approved

#31 by N. J. A. Sloane at Wed Dec 24 13:14:57 EST 2014

FORMULA

For n > 98, a(n) = n + 30. - Charles R Greathouse IV, Sep 02 2011 (This implies a(n+2) = 2*a(n+1)-a(n) for n > 98.)

STATUS

proposed

editing

#30 by Jon E. Schoenfield at Mon Dec 22 08:27:53 EST 2014

STATUS

editing

proposed