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Search: id:A057486
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| A057486 |
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Degrees of absolutely reducible trinomials, i.e. numbers n such that x^n + x^m + 1 is factorable for all m between 1 and n. |
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4
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| 8, 13, 16, 19, 24, 26, 27, 32, 37, 38, 40, 43, 45, 48, 50, 51, 53, 56, 59, 61, 64, 67, 69, 70, 72, 75, 77, 78, 80, 82, 83, 85, 88, 91, 96, 99, 101, 104, 107, 109, 112, 114, 115, 116, 117, 120, 122, 125, 128, 131, 133, 136, 138, 139, 141, 143, 144, 149, 152, 157
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
Index entries for sequences related to trinomials over GF(2)
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EXAMPLE
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a(1) = 8 because x^8 + x^1 + 1 = (1 + x + x^2)*(1 + x^2 + x^3 + x^5 + x^6) and x^8 + x^2 + 1 = (1 + x + x^4)^2 and x^8 + x^3 + 1 = (1 + x + x^3)*(1 + x + x^2 + x^3 + x^5) and x^8 + x^4 + 1 = (1 + x + x^2)^4 and x^8 + x^5 + 1 = (1 + x^2 + x^3)*(1 + x^2 + x^3 + x^4 + x^5) and x^8 + x^6 + 1 = (1 + x^3 + x^4)^2 and x^8 + x^7 + 1 = (1 + x + x^2)*(1 + x + x^3 + x^4 + x^6).
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MATHEMATICA
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Do[ k = 1; While[ ToString[ Factor[ x^n + x^k + 1, Modulus -> 2 ]] != ToString[ x^n + x^k + 1 ] && k < n, k++ ]; If[ k == n, Print[ n ]], {n, 2, 234} ]
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CROSSREFS
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Complement of A073571. Cf. A001153, A002475, A073639.
Sequence in context: A059194 A080361 A054295 this_sequence A129410 A070112 A070113
Adjacent sequences: A057483 A057484 A057485 this_sequence A057487 A057488 A057489
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 28 2000
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