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Numbers whose minimal (or greedy) Lucas representation (A130310) is palindromic.
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%I #8 Feb 21 2022 02:30:17

%S 0,2,6,9,13,20,24,31,49,56,64,78,100,125,136,150,158,169,201,237,252,

%T 324,342,364,378,396,404,422,444,523,581,606,650,708,845,874,910,932,

%U 961,975,1004,1040,1048,1077,1113,1135,1164,1366,1460,1500,1572,1666,1692,1786

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

%C 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 Amiram Eldar, <a href="/A351712/b351712.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>.

%e The first 10 terms are:

%e n a(n) A130310(a(n))

%e ---------------------

%e 1 0 0

%e 2 2 1

%e 3 6 1001

%e 4 9 10001

%e 5 13 100001

%e 6 20 1000001

%e 7 24 1001001

%e 8 31 10000001

%e 9 49 100000001

%e 10 56 100010001

%t 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 Cf. A000032, A000211, A130310.

%Y Subsequence of A054770.

%Y Similar sequences: A002113, A006995, A014190, A094202, A331191, A351717.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Feb 17 2022