A294923 Number n such that the whole sequence of the first n terms of A293700 is a palindrome.

1, 3, 5, 7, 9, 11, 13, 15, 17, 46, 83, 120, 157, 194, 231, 268, 305, 342, 379, 416, 453, 490, 527, 564, 601, 638, 675, 712, 749, 786, 823, 860, 897, 934, 971, 1008, 1045, 1082, 1119, 1156, 9105, 19792, 51817, 83842, 201253, 318664, 436075, 553486

Offset

1,2

Comments

A293700 are the first differences of A293698 which are the positive integers i such that floor(tan(i))=1.

A293701 are the lengths of the longest palindromic subsequences in the first n terms of A293700.

Links

Table of n, a(n) for n=1..48.

V.J. Pohjola, Line plot for n=1..50

Example

The first 3 terms of A293701 are (3,19,3) which is a palindromic sequence, so 3 is a term.
The first 4 terms of A293701 are (3,19,3,19) which is not a palindromic sequence, so 4 is not a term.
The first 17 terms of A293701 are (3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3) which is a palindromic sequence, so 17 is a term.
The first 18 terms of A293701 are (3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 3) which is not a palindromic sequence, so 18 is not a term.
The first 19 terms of A293701 are (3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 19, 3, 3, 16) which is not a palindromic sequence, so 19 is not a term.

Mathematica

rootsp7 = Flatten[Position[Table[Floor[Tan[n]], {n, 1, 10^7}], 1]];
difp7 = Differences[rootsp7];
nx = {}; Do[
If[Table[difp7[[i]], {i, 1, n}] == Reverse[Table[difp7[[i]], {i, 1, n}]],
  AppendTo[nx, n]], {n, 1, Length[difp7]}]
nx

Crossrefs

Cf. A293701, A293700, A293698, A294924.

Sequence in context: A143450 A225563 A373512 * A005842 A204458 A192861

Adjacent sequences: A294920 A294921 A294922 * A294924 A294925 A294926

Keyword

nonn

Author

V.J. Pohjola, Nov 11 2017

Status

approved