A295285 Numbers n such that for positive integers i, the union of sequences n+22i contains the positive roots of floor(tan(k)) = 1 (A293698).

1, 4, 183, 538, 893, 1248, 1603, 1958, 2313, 2668, 3023, 3378, 3733, 4088, 4443, 4798, 5153, 5508, 5863, 6218, 6573, 6928, 225919, 226274, 226629, 226984, 227339, 227694, 228049, 228404, 228759, 229114, 229469, 229824

Offset

1,2

Comments

Each number n is the first term of the corresponding individual sequence n+22i, and the whole is union of these overlapping sequences. Due to periodicity, there is a single generating function (n-(n-22)*j)/(j-1)^2 for the sequences. However, the function does not provide predictive means for generating A293698, because also terms which are not the roots are generated. The roots appear in each n+22i as finite subsequences of given length, at given steps. There is, however slight but difficult or impossible to predict variability both in the length, which is either 37 or 36, and the step which is either 7810 or 7832. A293698 is union of these subsequences. - V.J. Pohjola, Feb 25 2018

Links

V.J. Pohjola, Table of n, a(n) for n = 1..101

V. J. Pohjola, Line plot for n=1..3

V. J. Pohjola, Line plot for n=1..100

Example

For n = 1, i = 0..12, the terms 1, 23, 45, .., 265 are the roots.
For n = 4, i = 0..28, the terms 4, 26, 48, .., 620 are the roots.
For n = 183, i = 0..36, the terms 183, 205, 227, .., 975 are the roots.
For n = 1, i = 331..367, the terms 7283, 7305, 7327, .., 8075 are the roots.
For n = 4, i = 347..383, the terms 7638, 7660, 7682, .., 8430 are the roots.
For n = 183, i = 355..391, the terms 7993, 8015, 8037, .., 8785 are the roots.
The subsequences have the length of either 36 or 37 beyond the initial ranges 1+22i and 4+22i which are 13 and 29, respectively.

Mathematica

posroots6 = {}; Do[If[Floor[Tan[n]] == 1, AppendTo[posroots6, n]], {n, 0, 10^6}]
bigroots = {1}; posrootsi = {{1}}; Do[jj = {};
Do[lastb = Last[bigroots];
If[MemberQ[posroots6, lastb + 22*j], AppendTo[jj, j]], {j, 0, 10^4}];
posrootsi = Flatten[AppendTo[posrootsi, Table[lastb + 22*jj[[k]], {k, 1, Length[jj]}]]];
bigroot = First[Complement[posroots6, posrootsi]];
AppendTo[bigroots, bigroot], {i, 1, 100}]; bigroots

Crossrefs

Cf. A293698, A000503.

Sequence in context: A240282 A278693 A172018 * A322915 A221046 A024266

Adjacent sequences: A295282 A295283 A295284 * A295286 A295287 A295288

Keyword

nonn

Author

V.J. Pohjola, Nov 19 2017

Extensions

Name edited by V.J. Pohjola, Mar 15 2018

Status

approved