This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A088306 #47 Mar 07 2021 00:11:19 %S A088306 1,-2,-11,-33,-52174,260515,-573204,37362253,-42781604,122925461, %T A088306 534483448,3083975227,902209779836,-2685575996367,-65398140378926, %U A088306 74357078147863,214112296674652,642336890023956,-5920787228742393,-12055686754159438,18190586279576483,-48436859313312404 %N A088306 Integers n with tan n > |n|, ordered by |n|. %C A088306 Name was "Positive integers n with |tan n| > n." before signs were added. The sign here shows whether tan(|n|) is positive or negative. %C A088306 That this sequence is infinite was proved by Bellamy, Lagarias and Lazebnik. It seems not to be known whether there are infinitely many n with tan n > n. %C A088306 At approximately 2.37e154, there is a value of n which has tan(n)/n > 556. - _Phil Carmody_, Mar 04 2007 [This is index 214 in the b-file.] %C A088306 As n increases, log(|a(n)|)/n seems to approach Pi/2; this is similar to what would be expected if an integer sequence were created by drawing many random numbers independently from a uniform distribution on the interval [-Pi/2,+Pi/2] and including in the sequence only those integers j for which the j-th random number x_j happened to satisfy |x_j| < 1/j (and applying to j the sign of x_j). - _Jon E. Schoenfield_, Aug 19 2014; updated Nov 07 2014 to reflect the change in the sequence's Name) %H A088306 Jon E. Schoenfield, <a href="/A088306/b088306.txt">Table of n, a(n) for n = 1..1000</a> %H A088306 D. Bellamy, J. C. Lagarias and F. Lazebnik, <a href="http://www.math.udel.edu/~lazebnik/papers/tan_n.pdf">Proposed problem: large values of Tan n</a> %H A088306 Jon E. Schoenfield, <a href="/A088306/a088306_3.txt">Magma program</a> %p A088306 a:=proc(n) if abs(evalf(tan(n)))>n then n else fi end: seq(a(n),n=1..100000); # _Emeric Deutsch_, Dec 18 2004 %t A088306 Select[Range[600000],Abs[Tan[#]]>#&] (* _Harvey P. Dale_, Nov 30 2012 *) %o A088306 (PARI) is(n)=tan(n)>abs(n) \\ _Charles R Greathouse IV_, Nov 07 2014 %Y A088306 Cf. A000503, A224269, A079330, A088989. %Y A088306 Cf. A249836 (subsequence of positive terms). %K A088306 sign %O A088306 1,2 %A A088306 _Paul Boddington_, Nov 05 2003 %E A088306 More terms from _Jon E. Schoenfield_, Aug 17 2014 %E A088306 Signs added and other edits by _Franklin T. Adams-Watters_, Sep 09 2014