The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A228499 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A228499

Sums of two rational cubes, excluding cubes and twice cubes.
(history; published version)

#19 by Charles R Greathouse IV at Tue Jan 24 09:37:46 EST 2023

STATUS

editing

approved

#18 by Charles R Greathouse IV at Tue Jan 24 09:37:45 EST 2023

CROSSREFS

Cf. A020898, A060838. Subsequence of A020897, and hence of A159843.

Cf. A020898, A060838.

STATUS

approved

editing

#17 by Michael Somos at Sat Feb 29 18:47:12 EST 2020

STATUS

editing

approved

#16 by Michael Somos at Sat Feb 29 18:47:00 EST 2020

COMMENTS

These are all the integers A>0 such that the rank of the elliptic curve x^3 + y^3 = A is positive (A060838(A)>0). - Michael Somos, Feb 29 2020

CROSSREFS

Cf. A020898, A060838. Subsequence of A159843.

STATUS

approved

editing

Discussion

Sat Feb 29

18:47

Michael Somos: Added more info.

#15 by Bruno Berselli at Tue Jan 19 09:27:08 EST 2016

STATUS

proposed

approved

#14 by Arkadiusz Wesolowski at Tue Jan 19 09:07:18 EST 2016

STATUS

editing

proposed

#13 by Arkadiusz Wesolowski at Tue Jan 19 09:06:38 EST 2016

COMMENTS

Any number of these Each term can be written as sum of two rational cubes infinitely many times.

PROG

(PARI) for(n=1, 124, if(ellanalyticrank(ellinit([0, (4*n)^2]))[1]>0, print1(n, ", ")));

/* It's not sure that the program works for n > 124 */

for(n=1, 124, if(ellanalyticrank(ellinit([0, (4*n)^2]))[1]>0, print1(n, ", ")));

STATUS

approved

editing

Discussion

Tue Jan 19

09:07

Arkadiusz Wesolowski: cosmetic change

#12 by Wolfdieter Lang at Tue Oct 13 13:33:58 EDT 2015

STATUS

reviewed

approved

#11 by Danny Rorabaugh at Tue Oct 13 12:40:11 EDT 2015

STATUS

proposed

reviewed

#10 by Danny Rorabaugh at Tue Oct 13 12:40:07 EDT 2015

STATUS

editing

proposed