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A071428
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Numbers n such that x^n + x^(n-1) + x^(n-2) + ... + x + 1 is irreducible over GF(3).
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0
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4, 6, 16, 18, 28, 30, 42, 52, 78, 88, 100, 112, 126, 136, 138, 148, 162, 172, 196, 198, 210, 222, 232, 256, 268, 280, 282, 292, 316, 330, 352, 378, 388, 400, 448, 460, 462, 486, 508, 520, 556, 568, 570, 592, 606, 616, 630, 640, 652, 676, 690, 700, 738, 750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| n such that n+1 is a prime with primitive root 3 (A019334 except for the first term). [Joerg Arndt, Jul 05 2011]
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MATHEMATICA
| Do[s = Sum[x^i, {i, 0, n}]; If[ ToString[ Factor[s, Modulus -> 3]] == ToString[s], Print[n]], {n, 0, 800, 2}]
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PROG
| (PARI) for(n=2, 1000, if(polisirreducible(Mod(1, 3)*sum(e=0, n, x^e)), print1(n+1, ", "))) /* or: */
forprime(p=5, 1000, if(znorder(Mod(3, p))==p-1, print1(p-1, ", "))) /* much faster */
/* Joerg Arndt, Jul 05 2011 */
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CROSSREFS
| Cf. A071642.
Sequence in context: A056222 A186201 A138624 * A117988 A120542 A132344
Adjacent sequences: A071425 A071426 A071427 * A071429 A071430 A071431
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KEYWORD
| easy,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 22 2002
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