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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).

%I A295285 #29 Mar 26 2018 21:01:05
%S A295285 1,4,183,538,893,1248,1603,1958,2313,2668,3023,3378,3733,4088,4443,
%T A295285 4798,5153,5508,5863,6218,6573,6928,225919,226274,226629,226984,
%U A295285 227339,227694,228049,228404,228759,229114,229469,229824
%N 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).
%C A295285 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
%H A295285 V.J. Pohjola, <a href="/A295285/b295285.txt">Table of n, a(n) for n = 1..101</a>
%H A295285 V. J. Pohjola, <a href="https://palindromesdotblog.files.wordpress.com/2018/02/bigroots-1-3-a295285.pdf">Line plot for n=1..3</a>
%H A295285 V. J. Pohjola, <a href="https://palindromesdotblog.files.wordpress.com/2018/02/bigroots-1-100-a295285.pdf">Line plot for n=1..100</a>
%e A295285 For n = 1, i = 0..12, the terms 1, 23, 45, .., 265 are the roots.
%e A295285 For n = 4, i = 0..28, the terms 4, 26, 48, .., 620 are the roots.
%e A295285 For n = 183, i = 0..36, the terms 183, 205, 227, .., 975 are the roots.
%e A295285 For n = 1, i = 331..367, the terms 7283, 7305, 7327, .., 8075 are the roots.
%e A295285 For n = 4, i = 347..383, the terms 7638, 7660, 7682, .., 8430 are the roots.
%e A295285 For n = 183, i = 355..391, the terms 7993, 8015, 8037, .., 8785 are the roots.
%e A295285 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.
%t A295285 posroots6 = {}; Do[If[Floor[Tan[n]] == 1, AppendTo[posroots6, n]], {n, 0, 10^6}]
%t A295285 bigroots = {1}; posrootsi = {{1}}; Do[jj = {};
%t A295285 Do[lastb = Last[bigroots];
%t A295285 If[MemberQ[posroots6, lastb + 22*j], AppendTo[jj, j]], {j, 0, 10^4}];
%t A295285 posrootsi = Flatten[AppendTo[posrootsi, Table[lastb + 22*jj[[k]], {k, 1, Length[jj]}]]];
%t A295285 bigroot = First[Complement[posroots6, posrootsi]];
%t A295285 AppendTo[bigroots, bigroot], {i, 1, 100}]; bigroots
%Y A295285 Cf. A293698, A000503.
%K A295285 nonn
%O A295285 1,2
%A A295285 _V.J. Pohjola_, Nov 19 2017
%E A295285 Name edited by _V.J. Pohjola_, Mar 15 2018