

A088306


Integers n with tan n > n, ordered by n.


3



1, 2, 11, 33, 52174, 260515, 573204, 37362253, 42781604, 122925461, 534483448, 3083975227, 902209779836, 2685575996367, 65398140378926, 74357078147863, 214112296674652, 642336890023956, 5920787228742393, 12055686754159438, 18190586279576483, 48436859313312404
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OFFSET

1,2


COMMENTS

Name was "Positive integers n with tan n > n." before signs were added. The sign here shows whether tan(n) is positive or negative.
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.
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 bfile.]
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 jth 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)


LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 1..1000
D. Bellamy, J. C. Lagarias and F. Lazebnik, Proposed problem: large values of Tan n
Jon E. Schoenfield, Magma program


MAPLE

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


MATHEMATICA

Select[Range[600000], Abs[Tan[#]]>#&] (* Harvey P. Dale, Nov 30 2012 *)


PROG

(PARI) is(n)=tan(n)>abs(n) \\ Charles R Greathouse IV, Nov 07 2014


CROSSREFS

Cf. A000503, A224269, A079330, A088989.
Sequence in context: A034427 A056368 A056359 * A100109 A328152 A209033
Adjacent sequences: A088303 A088304 A088305 * A088307 A088308 A088309


KEYWORD

sign


AUTHOR

Paul Boddington, Nov 05 2003


EXTENSIONS

More terms from Jon E. Schoenfield, Aug 17 2014
Signs added and other edits by Franklin T. AdamsWatters, Sep 09 2014


STATUS

approved



