| DATA
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0, 2, 6, 9, 13, 20, 24, 31, 49, 56, 64, 78, 100, 125, 136, 150, 158, 169, 201, 237, 252, 324, 342, 364, 378, 396, 404, 422, 444, 523, 581, 606, 650, 708, 845, 874, 910, 932, 961, 975, 1004, 1040, 1048, 1077, 1113, 1135, 1164, 1366, 1460, 1500, 1572, 1666, 1692, 1786
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| MATHEMATICA
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lucasPalQ[n_] := Module[{s = {}, m = n, k = 1}, While[m > 0, If[m == 1, k = 1; AppendTo[s, k]; m = 0, If[m == 2, k = 0; AppendTo[s, k]; m = 0, While[LucasL[k] <= m, k++]; k--; AppendTo[s, k]; m -= LucasL[k]; k = 1]]]; PalindromeQ[IntegerDigits[Total[2^s], 2]]]; Select[Range[0, 2000], lucasPalQ]
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