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A158032 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. 0
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; refs; listen; history; text; internal format)
OFFSET

0,14

COMMENTS

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

LINKS

Table of n, a(n) for n=0..50.

FORMULA

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)))

MATHEMATICA

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}]

CROSSREFS

Sequence in context: A288183 A324055 A087664 * A282886 A282846 A326129

Adjacent sequences:  A158029 A158030 A158031 * A158033 A158034 A158035

KEYWORD

sign,uned

AUTHOR

Roger L. Bagula, Mar 11 2009

STATUS

approved

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Last modified October 21 05:28 EDT 2021. Contains 348141 sequences. (Running on oeis4.)