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A087481
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Number of polynomials of the form x^n +- x^(n-1) +- x^(n-2) +- ... +- 1 irreducible over the integers.
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2
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2, 4, 4, 16, 12, 48, 64, 192, 260, 1024, 1128, 4096, 4480, 13310, 20620, 65434, 76376, 262144
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For each n, there are 2^n polynomials to consider. All 2^n polynomials are irreducible for n = 1, 2, 4, 10, 12, 18, which is sequence A071642. For those values of n, n+1 is a prime in Artin's primitive root conjecture (A001122).
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LINKS
| Eric Weisstein's World of Mathematics, Irreducible Polynomial
Math Overflow, Irreducible polynomials with constrained coefficients [From T. D. Noe (noe(AT)sspectra.com), Dec 11 2009]
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MATHEMATICA
| Irreducible[p_, n_] := Module[{f}, f=FactorList[p, Modulus->n]; Length[f]==1 || Simplify[p-f[[2, 1]]]===0]; Table[xx=x^Range[0, n-1]; cnt=0; Do[p=x^n+xx.(2*IntegerDigits[i, 2, n]-1); If[Irreducible[p, 0], cnt++ ], {i, 0, 2^n-1}]; cnt, {n, 18}]
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CROSSREFS
| Cf. A001122, A071642, A087482 (irreducible binary polynomials).
Sequence in context: A117291 A079102 A071337 * A038210 A176739 A154919
Adjacent sequences: A087478 A087479 A087480 * A087482 A087483 A087484
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Sep 09 2003
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