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%I #7 Feb 21 2022 02:30:03
%S 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 107,115,122,128,150,166,176,198,200,211,219,233,244,246,260,271,277,
%U 288,296,310,321,345,360,396,405,441,469,484,520,522,544,562,570,588
%N Numbers whose maximal (or lazy) Lucas representation (A130311) is palindromic.
%C 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 Amiram Eldar, <a href="/A351717/b351717.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) A130311(a(n))
%e ----------------------
%e 1 0 0
%e 2 2 1
%e 3 3 11
%e 4 5 101
%e 5 6 111
%e 6 10 1111
%e 7 12 10101
%e 8 14 11011
%e 9 17 11111
%e 10 20 101101
%t 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 Cf. A000032, A001610, A130311.
%Y Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Feb 17 2022