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Search: id:A158032
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| A158032 |
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Coefficients of the polynomial from factoring (x^167+1)/(x+1) modulo 2 gives: p(x)=1 + x + x^4 + x^6 + x^8 + x^10 + x^12 + x^13 + x^17 + x^19 + x^23 + x^24 + x^25 + x^26 + x^27 + x^29 + x^31 + x^32 + x^33 + x^35 + x^36 + x^40 + x^42 + x^45 + x^46 + x^47 + x^49 + x^50 + x^52 + x^53 + x^56 + x^59 + x^60 + x^62 + x^64 + x^67 + x^70 + x^71 + x^73 + x^76 + x^78 + x^81 + x^83. |
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1
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| 1, 0, -1, 0, 1, -1, -1, 1, 1, -1, -1, 1, 1, -2, -1, 4, 0, -5, 3, 5, -7, -4, 10, 1, -12, 2, 16, -6, -21, 13, 27, -29, -28, 52, 19, -77, 4, 97, -40, -110, 85, 119, -143, -119, 230, 95, -354, -16, 499, -159, -622
(list; graph; listen)
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OFFSET
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0,14
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COMMENT
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Primes of the type 11,23,83,107,167...
Flatten[Table[If[PrimeQ[n] && PrimeQ[10*n - 1] && PrimeQ[( n - 1)/2], n, {}], {n, 1, 10000}]]
that gives nearly equal factorizations:
Factor[(x^Prime+1)/(x+1),Modulus->2]=f1(x)*f2(x);
and the power of factor is the next lower prime:
23->11;
167->83
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FORMULA
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p(x)=1 + x + x^4 + x^6 + x^8 + x^10 + x^12 + x^13 + x^17 +
x^19 + x^23 + x^24 + x^25 + x^26 + x^27 + x^29 + x^31 +
x^32 + x^33 + x^35 + x^36 + x^40 + x^42 + x^45 + x^46 +
x^47 + x^49 + x^50 + x^52 + x^53 + x^56 + x^59 + x^60 +
x^62 + x^64 + x^67 + x^70 + x^71 + x^73 + x^76 + x^78 +
x^81 + x^83;
a(n)=coefficients(1/(x^83*p(1/x)))
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MATHEMATICA
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f[x_] = FactorList[PolynomialMod[(x^167 + 1)/((x + 1)), 2], Modulus -> 2][[2]][[1]];
g[x] = ExpandAll[x^83*f[1/x]];
a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]
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CROSSREFS
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Sequence in context: A158285 A059781 A087664 this_sequence A120112 A103977 A109883
Adjacent sequences: A158029 A158030 A158031 this_sequence A158033 A158034 A158035
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 11 2009
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