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MATHEMATICA
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Clear[m] NSolve[x^5-x^4-x^3-x^2-x-1==0, x] k=1.96594823664548545 q=k^2-k-1/k-1/k^2-1/k^3 m0={{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 1, q}} m[n_]=MatrixPower[m0, n]; a=Table[If[Mod[Floor[Re[m[n][[5, 5]]]], 2]==1, Floor[Re[m[n][[5, 5]]]], Floor[Re[m[n][[5, 5]]]]+1], {n, 1, digits}]; b=Table[If[PrimeQ[a[[n]]]==True, a[[n]], 0], {n, 1, digits}] c=Delete[Union[b], 1]
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