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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.)