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 b-file.]
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)
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
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. Adams-Watters, Sep 09 2014
STATUS
approved