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Numbers whose maximal (or lazy) Lucas representation (A130311) is palindromic.
13

%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