The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A219726

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A219726

Integers of the form x^3 + 2y^3 (x, y > 0).
(history; published version)

#19 by Charles R Greathouse IV at Tue Apr 07 22:10:31 EDT 2020

STATUS

editing

approved

#18 by Charles R Greathouse IV at Tue Apr 07 22:10:13 EDT 2020

PROG

(PARI) is(n)=for(y=1, sqrtnint(lim/2)^(n-1/)\2, 3), if(ispower(n-2*y^3, 3), return(1))); 0 \\ Charles R Greathouse IV, Nov 26 2012Apr 07 2020

(PARI) list(lim)=my(v=List(), Y); lim\=1; for(y=1, sqrtnint((lim-1)\2, 3), Y=2*y^3; for(x=1, sqrtnint(lim-Y, 3), listput(v, x^3+Y))); Set(v) \\ Charles R Greathouse IV, Apr 07 2020

STATUS

proposed

editing

#17 by Bernard Schott at Tue Apr 07 17:23:58 EDT 2020

STATUS

editing

proposed

#16 by Bernard Schott at Tue Apr 07 17:21:26 EDT 2020

LINKS

D. R. Heath-Brown, <a href="https://projecteuclid.org/euclid.acta/1485891369">Primes represented by x^3 + 2y^3</a>, Acta Mathematica 186 (2001), pp. 1-84.

STATUS

proposed

editing

Discussion

Tue Apr 07

17:23

Bernard Schott: Put the link with the proof in Acta Mathematica here because the link seems no good in A173587.

#15 by Michel Marcus at Tue Apr 07 16:55:35 EDT 2020

STATUS

editing

proposed

Discussion

Tue Apr 07

17:00

Bernard Schott: Yes Michel, thanks.

#14 by Michel Marcus at Tue Apr 07 16:55:21 EDT 2020

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Roger_Heath-Brown">David Rodney "Roger" Heath-Brown</a>

STATUS

proposed

editing

Discussion

Tue Apr 07

16:55

Michel Marcus: the article title is "Roger Heath-Brown"

#13 by Bernard Schott at Tue Apr 07 16:48:37 EDT 2020

STATUS

editing

proposed

#12 by Bernard Schott at Tue Apr 07 16:48:23 EDT 2020

COMMENTS

D. R. Heath-Brown proved in 2001 that there are infinitely many prime numbers in this sequence. These primes are in A173587. - _Bernard Schott_, Apr 07 2020

STATUS

proposed

editing

#11 by Bernard Schott at Tue Apr 07 16:41:02 EDT 2020

STATUS

editing

proposed

#10 by Bernard Schott at Tue Apr 07 16:38:56 EDT 2020

LINKS

Wikipédia, Wikipedia, <a href="https://en.wikipedia.org/wiki/Roger_Heath-Brown">David Rodney "Roger" Heath-Brown</a>

Discussion

Tue Apr 07

16:40

Bernard Schott: One comment and one link.