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 A293702 a(n) is the length of the longest palindromic subsequence in the first n terms of A293751. 11
 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)
 OFFSET 1,3 LINKS V.J. Pohjola, Table of n, a(n) for n = 1..10000 V.J. Pohjola, Line plot for n=1…30 V.J. Pohjola, Line plot for n=1...10000 EXAMPLE 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. MATHEMATICA 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]] *) CROSSREFS Cf. A293698, A293751, A293700, A293701, A293705, A293704, A293699, A293703, A293706. Sequence in context: A069902 A085779 A078936 * A061794 A088524 A129337 Adjacent sequences:  A293699 A293700 A293701 * A293703 A293704 A293705 KEYWORD nonn AUTHOR V.J. Pohjola, Oct 16 2017 STATUS approved

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Last modified October 22 22:22 EDT 2020. Contains 337962 sequences. (Running on oeis4.)