1,2

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.

Next term is greater than 10^7. - Ryan Propper (rpropper(AT)stanford.edu), Sep 04 2005

Comment from Phil Carmody (pc+oeis(AT)asdf.org), Mar 04 2007: (Start) The following n, tan(n) pairs are in the sequence, but I make no claim that there are no others in between.

37362253 37754853.361

42781604 -85369290.412

122925461 326900723.479

534483448 1914547468.536

3083975227 13356993783.764

902209779836 1893164438251.901

2685575996367 -5926554327084.648

65398140378926 -68524021915772.619

74357078147863 134654932852015.499

214112296674652 3855691461342749.077

5920787228742393 -6082806669126598.307

At approximately 2.37e154, there is a value of n which has tan(n)/n > 556. (End)

D. Bellamy, J. C. Lagarias and F. Lazebnik, Proposed problem: large values of Tan n

a:=proc(n) if abs(evalf(tan(n)))>n then n else fi end: seq(a(n), n=1..100000); (E. Deutsch)

Cf. A000503.

Sequence in context: A034427 A056368 A056359 this_sequence A100109 A026961 A026971

Adjacent sequences: A088303 A088304 A088305 this_sequence A088307 A088308 A088309

hard,nonn

Paul Boddington (psb(AT)maths.warwick.ac.uk), Nov 05 2003