A294924 Numbers n such that the whole sequence of the first n terms of A293699 is a palindrome.

1, 3, 5, 7, 26, 63, 100, 137, 174, 211, 248, 285, 322, 359, 396, 433, 470, 507, 544, 581, 618, 655, 692, 729, 766, 803, 840, 877, 914, 951, 988, 1025, 1062, 1099, 1136, 1173, 1210, 1247, 1284, 1321, 1358, 1395, 1432, 1469, 1506, 1543, 1580, 1617, 1654, 1691, 1728, 1765, 1802, 1839, 1876, 1913, 1950, 1987, 2024, 2061, 2098, 2135

Offset

1,2

Comments

A293699 are the first differences of A293751 which are the positive integers i such that floor(tan(-i))=1.

A293702 are the lengths of the longest palindromic subsequences in the first n terms of A293699.

Links

Table of n, a(n) for n=1..62.

V.J. Pohjola, Line plot for n=1..7

V.J. Pohjola, Line plot for n=1..85

Example

The first 7 terms of A293699 are (3, 19, 3, 19, 3, 19, 3) which is a palindromic sequence, so 7 is a term.
The first 8 terms of A293699 are (3, 19, 3, 19, 3, 19, 3, 3) which is not a palindromic sequence, so 8 is not a term.
The first 9 terms of A293699 are (3, 19, 3, 19, 3, 19, 3, 3, 16) which is not a palindromic sequence, so 9 is not a term.
The first 25 terms of A293699 are (3, 19, 3, 19, 3, 19, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3, 19, 3, 19, 3, 19) which is not a palindromic sequence, so 25 is not a term.
The first 26 terms of A293699 are (3, 19, 3, 19, 3, 19, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3, 16, 3, 3, 19, 3, 19, 3, 19, 3) which is a palindromic sequence, so 26 is a term.

Mathematica

rootsn7 = Flatten[Position[Table[Floor[Tan[-n]], {n, 1, 10^7}], 1]];
difn7 = Differences[rootsn7];
ny = {}; Do[
If[Table[difn7[[i]], {i, 1, n}] == Reverse[Table[difn7[[i]], {i, 1, n}]],
  AppendTo[ny, n]], {n, 1, Length[difn7]}]
ny

Crossrefs

Cf. A293702, A293699, A293751, A294923.

Sequence in context: A098475 A131039 A362684 * A249544 A027449 A126670

Adjacent sequences: A294921 A294922 A294923 * A294925 A294926 A294927

Keyword

nonn

Author

V.J. Pohjola, Nov 11 2017

Status

approved