The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A247857 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A247857

Primes of the form a^2 + b^4, with repetition.
(history; published version)

#29 by Bruno Berselli at Mon Oct 05 09:19:36 EDT 2015

STATUS

editing

approved

#28 by Bruno Berselli at Mon Oct 05 09:19:30 EDT 2015

CROSSREFS

Cf. A256852, A000040, A256852.

STATUS

proposed

editing

#27 by Jonathan Sondow at Mon Oct 05 09:13:16 EDT 2015

STATUS

editing

proposed

#26 by Jonathan Sondow at Mon Oct 05 09:12:50 EDT 2015

COMMENTS

No, by the uniqueness part of Fermat's two-squares theorem, at most one duplicate of a^2 + b^4 can exist. Namely, when a is a square, say a = B^2, then a^2 + b^4 = A^2 + B^4 where A = b^2. (This also proves Marcus's comment, since a^2 + b^4 = b^4 + B^4.) - Jonathan Sondow, Oct 03 2015

CROSSREFS

Cf. A256852, A000040, A002645.

STATUS

approved

editing

Discussion

Mon Oct 05

09:13

Jonathan Sondow: Removed duplicate Crossref A002645.

#25 by Michel Marcus at Sun Oct 04 03:51:54 EDT 2015

STATUS

reviewed

approved

#24 by Joerg Arndt at Sun Oct 04 02:29:09 EDT 2015

STATUS

proposed

reviewed

#23 by Michel Marcus at Sun Oct 04 01:39:32 EDT 2015

STATUS

editing

proposed

#22 by Michel Marcus at Sun Oct 04 01:39:23 EDT 2015

LINKS

John Friedlander and Henryk Iwaniec, <a href="http://www.pnas.org/cgi/content/full/94/4/1054">Using a parity-sensitive sieve to count prime values of a polynomial</a>, PNAS, vol. 94 no. 4, pp. 1054-1058.

#21 by Michel Marcus at Sun Oct 04 01:36:09 EDT 2015

LINKS

Marek Wolf, <a href="http://arxiv.org/abs/1003.4015">Continued fractions constructed from prime numbers</a>, arxiv.org/abs/arXiv:1003.4015, [math.NT], 2010, p. 8.

STATUS

proposed

editing

#20 by Jonathan Sondow at Sat Oct 03 23:06:37 EDT 2015

STATUS

editing

proposed