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A351712
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Numbers whose minimal (or greedy) Lucas representation (A130310) is palindromic.
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13
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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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OFFSET
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1,2
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COMMENTS
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A000211(n) = Lucas(n) + 2 is a term for all n > 2, since the representation of Lucas(n) + 2 is 10...01 with n-1 0's between the two 1's.
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LINKS
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EXAMPLE
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The first 10 terms are:
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1 0 0
2 2 1
3 6 1001
4 9 10001
5 13 100001
6 20 1000001
7 24 1001001
8 31 10000001
9 49 100000001
10 56 100010001
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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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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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