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A293702
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a(n) is the length of the longest palindromic subsequence in the first n terms of A293751.
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11
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1, 1, 3, 3, 5, 5, 7, 7, 7, 7, 7, 7, 7, 8, 8, 9, 11, 11, 12, 14, 16, 18, 20, 22, 24, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 63, 63, 63, 63, 63, 63, 63
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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EXAMPLE
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For n = 1, Roots = 18, 21; First differences = 3; Longest palindrome = 3; a(n) = 1.
For n = 2, Roots = 18, 21, 40; First differences = 3, 19; Longest palindrome = 3; a(n) = 1.
For n = 3, Roots = 18, 21, 40, 43; First differences = 3, 19, 3; Longest palindrome = 3, 19, 3; a(n) = 3.
For n = 20, Roots = 18, 21, 40, 43, 62, 65, 84, 87, 90, 106, 109, 112, 128, 131,134, 150, 153, 156, 172, 175; First differences = 3, 19, 3, 19, 3, 19, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3; Longest palindrome = 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3; a(n) = 14.
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MATHEMATICA
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rootsn = Flatten[Position[Table[Floor[Tan[-i]], {i, 1, 10^4}], 1]];
difn = Differences[rootsn];
imax = 100; palsn = {}; lenpalsn = {0};
Do[diffin = difn[[1 ;; i]]; lendiffin = Length[diffin];
pmax = i - Last[lenpalsn];
t = Table[difn[[p ;; i]], {p, 1, pmax}];
sn = Flatten[Select[t, # == Reverse[#] &]];
If[sn == {},
AppendTo[palsn, Last[palsn]] && AppendTo[lenpalsn, Last[lenpalsn]],
AppendTo[palsn, sn] && AppendTo[lenpalsn, Length[Flatten[sn]]]], {i, 1, imax}];
Drop[lenpalsn, 1] (* a(n)=Drop[lenpalsn, 1][[n]] *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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