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A351717 Numbers whose maximal (or lazy) Lucas representation (A130311) is palindromic.

%I A351717 #7 Feb 21 2022 02:30:03
%S A351717 0,2,3,5,6,10,12,14,17,20,28,30,34,36,42,46,56,61,75,77,85,92,94,101,
%T A351717 107,115,122,128,150,166,176,198,200,211,219,233,244,246,260,271,277,
%U A351717 288,296,310,321,345,360,396,405,441,469,484,520,522,544,562,570,588
%N A351717 Numbers whose maximal (or lazy) Lucas representation (A130311) is palindromic.
%C A351717 A001610(n) = Lucas(n+1) - 1 is a term for all n, since A001610(0) = 0 has the representation 0 and the representation of Lucas(n+1) - 1 is n 1's for n > 0.
%H A351717 Amiram Eldar, <a href="/A351717/b351717.txt">Table of n, a(n) for n = 1..10000</a>
%H A351717 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>.
%e A351717 The first 10 terms are:
%e A351717    n  a(n)  A130311(a(n))
%e A351717    ----------------------
%e A351717    1   0               0
%e A351717    2   2               1
%e A351717    3   3              11
%e A351717    4   5             101
%e A351717    5   6             111
%e A351717    6  10            1111
%e A351717    7  12           10101
%e A351717    8  14           11011
%e A351717    9  17           11111
%e A351717   10  20          101101
%t A351717 lazy = Select[IntegerDigits[Range[6000], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[# * Reverse @ LucasL[Range[0, Length[#] - 1]]] & /@ lazy; s = FromDigits /@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]; Join[{0}, Position[s, _?PalindromeQ] // Flatten]
%Y A351717 Cf. A000032, A001610, A130311.
%Y A351717 Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712.
%K A351717 nonn,base
%O A351717 1,2
%A A351717 _Amiram Eldar_, Feb 17 2022