The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A001153 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A001153

Degrees of primitive irreducible trinomials: n such that 2^n - 1 is a Mersenne prime and x^n + x^k + 1 is a primitive irreducible polynomial over GF(2) for some k with 0 < k < n.
(history; published version)

#64 by Joerg Arndt at Mon Aug 06 05:22:50 EDT 2018

STATUS

reviewed

approved

#63 by Michel Marcus at Tue Jul 24 12:08:35 EDT 2018

STATUS

proposed

reviewed

#62 by Jon E. Schoenfield at Sat Jul 21 18:45:29 EDT 2018

STATUS

editing

proposed

#61 by Jon E. Schoenfield at Sat Jul 21 18:45:26 EDT 2018

COMMENTS

Further terms of the form +-3 (mod 8) are unlikely, as the only possibility of an irreducible trinomial for n == +-3 (mod 8) is (by Swan's theorem) x^n+x^2+1 (and its reciprocal); see the Ciet et al. and the Swan reference. [_- _Joerg Arndt_, Jan 06 2014]

The first Mersenne prime exponent not ruled out by Swan's theorem and yet not a member of this sequence is 57885161. [_- _Gord Palameta_, Jul 20 2018]

AUTHOR

N. J. A. Sloane.

STATUS

proposed

editing

#60 by Michel Marcus at Sat Jul 21 12:18:12 EDT 2018

STATUS

editing

proposed

#59 by Michel Marcus at Sat Jul 21 12:18:08 EDT 2018

COMMENTS

74207281 is also in the sequence. - Gord Palameta, Jul 20 2018

EXTENSIONS

Also in the sequence: n = 74207281. - Gord Palameta, Jul 20 2018

STATUS

proposed

editing

#58 by Gord Palameta at Fri Jul 20 03:44:46 EDT 2018

STATUS

editing

proposed

Discussion

Fri Jul 20

04:18

Michel Marcus: well, see https://oeis.org/wiki/Style_Sheet#Extensions

04:50

Gord Palameta: On the other hand, the definition at https://oeis.org/eishelp2.html#R2 allows for some things that are not mentioned at https://oeis.org/wiki/Style_Sheet#Extensions , so perhaps there is some flexibility in usage. But the main thing is consistency, so if you feel strongly, maybe you could add a note to the discussion at A000043, proposing the change there as well. However, if you do move those entries in A000043 to the Comments section, then in the future when the ordinal position of Mersenne primes number 48, 49 and 50 are finally determined with certainty, then someone will need to delete them from the Comments section and move them back to the Extensions section. So it seems better to just leave them in the Extensions section rather than moving them out and back in. Also, in the Extensions section they serve as an ongoing reminder to extend the sequence itself when the time comes to do so.

#57 by Michel Marcus at Fri Jul 20 03:36:32 EDT 2018

LINKS

Richard P. Brent and Paul Zimmerman, <a href="https://hal.inria.fr/hal-01378493/document">Twelve New Primitive Binary Trinomials</a>, HAL Id : hal-01378493.

STATUS

proposed

editing

Discussion

Fri Jul 20

03:37

Michel Marcus: rather link to HAL abstract

03:37

Michel Marcus: the extension line should rather go to comments

03:43

Gord Palameta: For the extension line, I imitated what was done in A000043. This is a future entry in the sequence but its ordinal position is not yet determined because there may still be undiscovered Mersenne prime exponents smaller than this.

#56 by Gord Palameta at Fri Jul 20 03:26:54 EDT 2018

STATUS

editing

proposed

#55 by Gord Palameta at Fri Jul 20 03:18:03 EDT 2018

COMMENTS

The first Mersenne prime exponent not ruled out by Swan's theorem and yet not a member of this sequence is 57885161. [Gord Palameta, Jul 20 2018]

LINKS

R. P. Brent, <a href="http://maths.anu.edu.au/~brent/trinom-old.html">Searching for primitive trinomials (mod 2)</a> (first, "old" page)

R. P. Brent, <a href="http://maths.anu.edu.au/~brent/trinom.html">Searching for primitive trinomials (mod 2)</a> (second, current page)

R. P. Brent, <a href="ftp://ftp.comlab.ox.ac.uk/pub/Documents/techpapers/Richard P. Brent and Paul Zimmerman, <a href="https:/trinom/tablehal.inria.txtfr/hal-01378493/document">Tables of trinomialsTwelve New Primitive Binary Trinomials</a> (outdated)

EXTENSIONS

Also in the sequence: n = 74207281. - Gord Palameta, Jul 20 2018

STATUS

approved

editing

Discussion

Fri Jul 20

03:26

Gord Palameta: The ftp link is dead and I could not find a replacement URL, so I deleted it since it was marked "outdated" in any case. The abstract of "Twelve New Primitive Binary Trinomials" supports the claim about 57885161. It is best to include links to both trinom-old.html and trinom.html pages, since they actually have rather different content despite having identical titles; they are not really old and new versions of the same page.