The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A057485 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A057485

Numbers k>7 such that x^k + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 is irreducible over GF(2).
(history; published version)

#21 by Michael De Vlieger at Thu Dec 08 07:29:56 EST 2022

STATUS

reviewed

approved

#20 by Joerg Arndt at Thu Dec 08 01:31:44 EST 2022

STATUS

proposed

reviewed

#19 by Lucas A. Brown at Wed Dec 07 11:36:23 EST 2022

STATUS

editing

proposed

#18 by Lucas A. Brown at Wed Dec 07 11:36:10 EST 2022

PROG

if (x^n + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1).is_irreducible(): print() # Lucas A. Brown, Dec 07 2022

#17 by Lucas A. Brown at Wed Dec 07 11:35:18 EST 2022

PROG

for n in count(108):

#16 by Lucas A. Brown at Wed Dec 07 11:34:53 EST 2022

COMMENTS

Any subsequent terms are > 10^6. - Lucas A. Brown, Dec 07 2022

#15 by Lucas A. Brown at Wed Dec 07 11:34:32 EST 2022

DATA

10, 12, 15, 18, 25, 31, 34, 52, 55, 57, 127, 172, 220, 300, 393, 492, 772, 807, 972, 1023, 1266, 1564, 2220, 2242, 3585, 5314, 7306, 8719, 10777, 23647, 26119, 33127, 48036, 48945, 59172, 68841, 131071, 214780, 236892, 265857, 341841, 563599, 841444, 901057

PROG

(SageMath) P.<x> = GF(2)[]

from itertools import count

for n in count(10):

print('\b'*42, n, end='', flush=True)

if (x^n + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1).is_irreducible(): print() # Lucas A. Brown, Dec 07 2022

KEYWORD

nonn,morehard

EXTENSIONS

a(26)-a(44) from Lucas A. Brown, Dec 07 2022

STATUS

approved

editing

#14 by Joerg Arndt at Fri Apr 17 07:46:53 EDT 2020

STATUS

editing

approved

#13 by Joerg Arndt at Fri Apr 17 07:46:50 EDT 2020

MATHEMATICA

Do[ If[ ToString[ Factor[ x^n + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, Modulus -> 2 ] ] == ToString[ x^n + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 ], Print[ n ] ], {n, 0, 700} ]

STATUS

proposed

editing

#12 by Michel Marcus at Wed Apr 15 13:05:52 EDT 2020

STATUS

editing

proposed