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A351717
Numbers whose maximal (or lazy) Lucas representation (A130311) is palindromic.
13
0, 2, 3, 5, 6, 10, 12, 14, 17, 20, 28, 30, 34, 36, 42, 46, 56, 61, 75, 77, 85, 92, 94, 101, 107, 115, 122, 128, 150, 166, 176, 198, 200, 211, 219, 233, 244, 246, 260, 271, 277, 288, 296, 310, 321, 345, 360, 396, 405, 441, 469, 484, 520, 522, 544, 562, 570, 588
OFFSET
1,2
COMMENTS
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.
EXAMPLE
The first 10 terms are:
n a(n) A130311(a(n))
----------------------
1 0 0
2 2 1
3 3 11
4 5 101
5 6 111
6 10 1111
7 12 10101
8 14 11011
9 17 11111
10 20 101101
MATHEMATICA
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]
CROSSREFS
Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712.
Sequence in context: A099350 A337218 A306296 * A191173 A240026 A213212
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Feb 17 2022
STATUS
approved