The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A338094 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A338094

Number of ways to write 2*n + 1 as x^2 + y^2 + z^2 + w^2 with x + y a positive power of two, where x, y, z, w are nonnegative integers with x <= y and z <= w.
(history; published version)

#24 by N. J. A. Sloane at Tue Jan 19 21:01:25 EST 2021

STATUS

proposed

approved

#23 by Michael De Vlieger at Tue Jan 19 18:50:46 EST 2021

STATUS

editing

proposed

#22 by Michael De Vlieger at Tue Jan 19 18:50:45 EST 2021

LINKS

Zhi-Wei Sun, <a href="https://arxiv.org/abs/2010.05775">Sums of four squares with certain restrictions</a>, arXiv:2010.05775 [math.NT], 2020.

STATUS

approved

editing

#21 by OEIS Server at Tue Oct 13 04:03:44 EDT 2020

LINKS

Zhi-Wei Sun, <a href="/A338094/b338094_1.txt">Table of n, a(n) for n = 1..10000</a>

#20 by Bruno Berselli at Tue Oct 13 04:03:44 EDT 2020

STATUS

proposed

approved

Discussion

Tue Oct 13

04:03

OEIS Server: Installed new b-file as b338094.txt.  Old b-file is now b338094_1.txt.

#19 by Zhi-Wei Sun at Sun Oct 11 07:14:43 EDT 2020

STATUS

editing

proposed

#18 by Zhi-Wei Sun at Sun Oct 11 07:14:25 EDT 2020

COMMENTS

We have verified the latter version of the conjecture for m up to 3*10^7.

STATUS

proposed

editing

#17 by Zhi-Wei Sun at Sun Oct 11 06:58:46 EDT 2020

STATUS

editing

proposed

#16 by Zhi-Wei Sun at Sun Oct 11 06:58:09 EDT 2020

COMMENTS

By Theorem 1.1(ii) of the author's IJNT paper, any positive integer can be written as x^2 + y^2 + z^2 + w^2 with x, y, z, w nonnegative integers and x - y a power of two (including 2^0 = 1).

#15 by Zhi-Wei Sun at Sun Oct 11 06:53:33 EDT 2020

LINKS

Zhi-Wei Sun, <a href="/A338094/b338094_1.txt">Table of n, a(n) for n = 1..600010000</a>

STATUS

proposed

editing