A293698 Values of positive integer i such that floor(tan(i)) = 1.

1, 4, 23, 26, 45, 48, 67, 70, 89, 92, 111, 114, 133, 136, 155, 158, 177, 180, 183, 199, 202, 205, 221, 224, 227, 243, 246, 249, 265, 268, 271, 290, 293, 312, 315, 334, 337, 356, 359, 378, 381, 400, 403, 422, 425, 444, 447, 466, 469, 488, 491, 510, 513, 532, 535, 538, 554, 557, 560, 576, 579, 582, 598, 601, 604, 620

Offset

1,2

Comments

The sequence is the first result in the chain of iteration leading to the ultimate sequence A258024.

Sequence terms are also the roots of A000503(i)=1, starting from i=1.

This is a subsequence of A258024 from which this differs for the first time at n=11, where a(11) = 111, while A258024(11) = 105, the term not included in this sequence. Note that A000503(105) = 4, a term which is included in this sequence. - Antti Karttunen, Oct 30 2017

Numbers k such that Pi/4 <= k - m*Pi < arctan(2) for some m. - Robert Israel, Nov 06 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The values of floor(tan(i)), starting from i=0, are given in A000503. Those i, for which floor(tan(i))=1 is true, are the roots of this equation. Thus the roots are the positions of 1 in A000503(i>0).
For n=1, i=1; a(1)=1.
For n=2, i=4; a(2)=4.
For n=3, i=23; a(3)=23.

Mathematica

rootsp = Flatten[Position[Table[Floor[Tan[i]], {i, 1, 10^6}], 1]
(*a(n) = rootsp[[n]]*)
Alternatively:
rootsp = {}; Do[If[Floor[Tan[n]] == 1, AppendTo[rootsp, n]], {n, 1, 10^6}]
rootsp (*a(n) = rootsp[[n]]*)
Select[ Range@ 622, Floor@ Tan@ # == 1 &] (* Robert G. Wilson v, Nov 06 2017 *)

Prog

(PARI) isok(n) = floor(tan(n)) == 1; \\ Michel Marcus, Oct 24 2017
(PARI) first(n) = {my(res = vector(n), i = 0, pi = [Pi, Pi], sols = [atan(1), atan(2)]); while(1, for(j = ceil(sols[1]), floor(sols[2]), i++; if(i>n, return(res)); res[i] = j); sols+=[Pi(), Pi()])} \\ David A. Corneth, Oct 24 2017

Crossrefs

Cf. A000503, A258024, A293751, A293700, A293701, A293704, A293699, A293702, A293705, A004112, A024814.

Sequence in context: A016485 A258024 A258203 * A160613 A131545 A030716

Adjacent sequences: A293695 A293696 A293697 * A293699 A293700 A293701

Keyword

nonn

Author

V.J. Pohjola, Oct 15 2017

Status

approved