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A072833
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Numbers that are congruent to 0, 5, 8, 9 mod 12.
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3
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0, 5, 8, 9, 12, 17, 20, 21, 24, 29, 32, 33, 36, 41, 44, 45, 48, 53, 56, 57, 60, 65, 68, 69, 72, 77, 80, 81, 84, 89, 92, 93, 96, 101, 104, 105, 108, 113, 116, 117, 120, 125, 128, 129, 132, 137, 140, 141, 144, 149, 152, 153, 156, 161, 164, 165, 168, 173, 176, 177, 180, 185, 188, 189
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OFFSET
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0,2
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COMMENTS
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The exponents occurring in the expansion of F_6(q^2) (see Ahlgren) or, equivalently, the norms of the vectors in the A*_5 lattice are all in this list and probably include all numbers in this list. - Andrey Zabolotskiy, Aug 14 2020
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LINKS
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FORMULA
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G.f.: x*(3*x^2-2*x+5) / ((x-1)^2*(x^2+1)). - Colin Barker, Jul 31 2013
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MATHEMATICA
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(* This program is based on the function F_6(q^2), so it is not proved that it generates all terms. *) f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[6, q_]:= ( -3*f[q, q]^5 + 5*f[q, q]^3*f[q^3, q^3]^2 + 15*f[q, q]*f[q^3, q^3]^4 + 15*f[q^3, q^3]^6/f[q, q] )/32; cfs = CoefficientList[Series[F[6, q], {q, 0, 500}], q]; Take[Pick[Range[Length[cfs]] - 1, Sign[Abs[cfs]], 1], 50] (* G. C. Greubel, Apr 16 2018 *)
Flatten[#+{0, 5, 8, 9}&/@(12*Range[0, 20])] (* Harvey P. Dale, Apr 10 2022 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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