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A351712 Numbers whose minimal (or greedy) Lucas representation (A130310) is palindromic.

%I A351712 #8 Feb 21 2022 02:30:17
%S A351712 0,2,6,9,13,20,24,31,49,56,64,78,100,125,136,150,158,169,201,237,252,
%T A351712 324,342,364,378,396,404,422,444,523,581,606,650,708,845,874,910,932,
%U A351712 961,975,1004,1040,1048,1077,1113,1135,1164,1366,1460,1500,1572,1666,1692,1786
%N A351712 Numbers whose minimal (or greedy) Lucas representation (A130310) is palindromic.
%C A351712 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.
%H A351712 Amiram Eldar, <a href="/A351712/b351712.txt">Table of n, a(n) for n = 1..10000</a>
%H A351712 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>.
%e A351712 The first 10 terms are:
%e A351712    n  a(n) A130310(a(n))
%e A351712    ---------------------
%e A351712    1   0               0
%e A351712    2   2               1
%e A351712    3   6            1001
%e A351712    4   9           10001
%e A351712    5  13          100001
%e A351712    6  20         1000001
%e A351712    7  24         1001001
%e A351712    8  31        10000001
%e A351712    9  49       100000001
%e A351712   10  56       100010001
%t A351712 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]
%Y A351712 Cf. A000032, A000211, A130310.
%Y A351712 Subsequence of A054770.
%Y A351712 Similar sequences: A002113, A006995, A014190, A094202, A331191, A351717.
%K A351712 nonn,base
%O A351712 1,2
%A A351712 _Amiram Eldar_, Feb 17 2022